{
  localUrl: '../page/underlying_set.html',
  arbitalUrl: 'https://arbital.com/p/underlying_set',
  rawJsonUrl: '../raw/3gz.json',
  likeableId: '2500',
  likeableType: 'page',
  myLikeValue: '0',
  likeCount: '3',
  dislikeCount: '0',
  likeScore: '3',
  individualLikes: [
    'EricBruylant',
    'MYass',
    'EricRogstad'
  ],
  pageId: 'underlying_set',
  edit: '15',
  editSummary: '',
  prevEdit: '14',
  currentEdit: '15',
  wasPublished: 'true',
  type: 'wiki',
  title: 'Underlying set',
  clickbait: '',
  textLength: '1290',
  alias: 'underlying_set',
  externalUrl: '',
  sortChildrenBy: 'likes',
  hasVote: 'false',
  voteType: '',
  votesAnonymous: 'false',
  editCreatorId: 'EricRogstad',
  editCreatedAt: '2016-06-17 23:33:00',
  pageCreatorId: 'NateSoares',
  pageCreatedAt: '2016-05-09 05:52:53',
  seeDomainId: '0',
  editDomainId: 'AlexeiAndreev',
  submitToDomainId: '0',
  isAutosave: 'false',
  isSnapshot: 'false',
  isLiveEdit: 'true',
  isMinorEdit: 'false',
  indirectTeacher: 'false',
  todoCount: '3',
  isEditorComment: 'false',
  isApprovedComment: 'true',
  isResolved: 'false',
  snapshotText: '',
  anchorContext: '',
  anchorText: '',
  anchorOffset: '0',
  mergedInto: '',
  isDeleted: 'false',
  viewCount: '71',
  text: '[summary: What do a [-3gd], a [-3rb], and a [ topological space] have in common? Each is a [-3jz] with some structure built on top of it, and in each case, we call the set the *underlying set*.]\n\n\nWhat do a [-3gd], a [-3rb], and a [ topological space] have in common? Each is a [-3jz] with some structure built on top of it, and in each case, we call the set the *underlying set*. %%note: A group is a set with an [3h7 operation], a poset is a set with an [3dt ordering], and a topological space is a set with a collection of subsets that satisfy a [ certain property].%%\n\n###Algebraic structures###\n\nAn [3gx algebraic structure] is a set equipped with operators that follow certain laws, such as a [3gd group], which is a pair $(X, \\bullet)$ where $X$ is a [3jz set] and $\\bullet$ is an operator that follows certain laws. Given an algebraic structure,  we can simply throw away the operators and recover the set ($X$, in this case), which is known as the "underlying set" of the structure.\n\nThe underlying set is sometimes known as the "carrier set." Some algebraic structures have more than one underlying set; for example, a vector space is an algebraic structure built out of a [481 field] of scalars and a [3h2 commutative group], in which case the term "underlying set" is ambiguous.',
  metaText: '',
  isTextLoaded: 'true',
  isSubscribedToDiscussion: 'false',
  isSubscribedToUser: 'false',
  isSubscribedAsMaintainer: 'false',
  discussionSubscriberCount: '2',
  maintainerCount: '2',
  userSubscriberCount: '0',
  lastVisit: '',
  hasDraft: 'false',
  votes: [],
  voteSummary: 'null',
  muVoteSummary: '0',
  voteScaling: '0',
  currentUserVote: '-2',
  voteCount: '0',
  lockedVoteType: '',
  maxEditEver: '0',
  redLinkCount: '0',
  lockedBy: '',
  lockedUntil: '',
  nextPageId: '',
  prevPageId: '',
  usedAsMastery: 'false',
  proposalEditNum: '0',
  permissions: {
    edit: {
      has: 'false',
      reason: 'You don't have domain permission to edit this page'
    },
    proposeEdit: {
      has: 'true',
      reason: ''
    },
    delete: {
      has: 'false',
      reason: 'You don't have domain permission to delete this page'
    },
    comment: {
      has: 'false',
      reason: 'You can't comment in this domain because you are not a member'
    },
    proposeComment: {
      has: 'true',
      reason: ''
    }
  },
  summaries: {},
  creatorIds: [
    'EricRogstad',
    'NateSoares',
    'AlexeiAndreev',
    'PatrickStevens'
  ],
  childIds: [],
  parentIds: [
    'abstract_algebra'
  ],
  commentIds: [
    '4j6'
  ],
  questionIds: [],
  tagIds: [
    'math2',
    'start_meta_tag',
    'needs_clickbait_meta_tag'
  ],
  relatedIds: [],
  markIds: [],
  explanations: [],
  learnMore: [],
  requirements: [],
  subjects: [],
  lenses: [],
  lensParentId: '',
  pathPages: [],
  learnMoreTaughtMap: {},
  learnMoreCoveredMap: {},
  learnMoreRequiredMap: {},
  editHistory: {},
  domainSubmissions: {},
  answers: [],
  answerCount: '0',
  commentCount: '0',
  newCommentCount: '0',
  linkedMarkCount: '0',
  changeLogs: [
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '19343',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-08-28 00:30:59',
      auxPageId: 'math2',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '19342',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'deleteTag',
      createdAt: '2016-08-28 00:30:31',
      auxPageId: 'formal_definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '19340',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'deleteTag',
      createdAt: '2016-08-28 00:30:20',
      auxPageId: '4bn',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '19338',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-08-28 00:29:43',
      auxPageId: 'start_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17130',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-07-19 02:08:20',
      auxPageId: 'needs_clickbait_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '14376',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'deleteTag',
      createdAt: '2016-06-22 17:30:08',
      auxPageId: 'needs_summary_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '2823',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '13791',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '15',
      type: 'newEdit',
      createdAt: '2016-06-17 23:33:00',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13790',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '14',
      type: 'newEdit',
      createdAt: '2016-06-17 23:31:03',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13789',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '13',
      type: 'newEdit',
      createdAt: '2016-06-17 23:30:19',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13788',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '12',
      type: 'newEdit',
      createdAt: '2016-06-17 23:29:57',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13759',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-06-17 23:18:00',
      auxPageId: 'formal_definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13757',
      pageId: 'underlying_set',
      userId: 'EricBruylant',
      edit: '0',
      type: 'deleteTag',
      createdAt: '2016-06-17 23:17:53',
      auxPageId: 'definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '2738',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '13611',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '11',
      type: 'newEdit',
      createdAt: '2016-06-17 17:50:56',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13601',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '9',
      type: 'newTag',
      createdAt: '2016-06-17 17:30:42',
      auxPageId: 'needs_summary_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '13597',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '9',
      type: 'newTag',
      createdAt: '2016-06-17 17:28:09',
      auxPageId: '4bn',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '12629',
      pageId: 'underlying_set',
      userId: 'PatrickStevens',
      edit: '9',
      type: 'newEdit',
      createdAt: '2016-06-14 12:29:59',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '11120',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '6',
      type: 'newEdit',
      createdAt: '2016-05-27 01:00:00',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10351',
      pageId: 'underlying_set',
      userId: 'EricRogstad',
      edit: '5',
      type: 'newEdit',
      createdAt: '2016-05-14 20:02:05',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10284',
      pageId: 'underlying_set',
      userId: 'AlexeiAndreev',
      edit: '4',
      type: 'newEdit',
      createdAt: '2016-05-14 00:31:42',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10121',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '3',
      type: 'newEdit',
      createdAt: '2016-05-12 18:58:59',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9938',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '2',
      type: 'newTag',
      createdAt: '2016-05-10 23:33:11',
      auxPageId: 'definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9695',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '2',
      type: 'newEdit',
      createdAt: '2016-05-09 05:54:26',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9694',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '0',
      type: 'newAlias',
      createdAt: '2016-05-09 05:53:14',
      auxPageId: '',
      oldSettingsValue: '3gz',
      newSettingsValue: 'underlying_set'
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9693',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteTag',
      createdAt: '2016-05-09 05:53:11',
      auxPageId: 'algebraic_structure',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9691',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '1',
      type: 'newEdit',
      createdAt: '2016-05-09 05:52:53',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9688',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-05-09 05:52:47',
      auxPageId: 'algebraic_structure',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '9687',
      pageId: 'underlying_set',
      userId: 'NateSoares',
      edit: '0',
      type: 'newParent',
      createdAt: '2016-05-09 05:49:35',
      auxPageId: 'abstract_algebra',
      oldSettingsValue: '',
      newSettingsValue: ''
    }
  ],
  feedSubmissions: [],
  searchStrings: {},
  hasChildren: 'false',
  hasParents: 'true',
  redAliases: {},
  improvementTagIds: [],
  nonMetaTagIds: [],
  todos: [],
  slowDownMap: 'null',
  speedUpMap: 'null',
  arcPageIds: 'null',
  contentRequests: {}
}