query: What is it, intuitively, that makes a structure "topological"?
positive_passages.docid: 28766
positive_passages.text: Intuition behind topological spaces
negative_passages.docid: 63214
negative_passages.text: Can continuity of inverse be omitted from the definition of topological group?
negative_passages.docid: 128481
negative_passages.text: Can two different topological spaces cover each other?
negative_passages.docid: 95897
negative_passages.text: Which sets occur as boundaries of other sets in topological spaces?
negative_passages.docid: 113688
negative_passages.text: Is Topological Space a Metric Space?
negative_passages.docid: 122410
negative_passages.text: Can one build a homology theory using submanifolds and their boundaries?
negative_passages.docid: 84104
negative_passages.text: Definition of neighborhood and open set in topology
negative_passages.docid: 108226
negative_passages.text: Are these bases for a topology?
negative_passages.docid: 60236
negative_passages.text: What is the difference between topological and metric spaces?
negative_passages.docid: 94246
negative_passages.text: Category-theoretic limit related to topological limit?
negative_passages.docid: 88823
negative_passages.text: How can the empty set be open in the definition of the cofinite topology?
negative_passages.docid: 70048
negative_passages.text: In which topologies do open sets maintain open under countable or arbitrary intersection?
negative_passages.docid: 81122
negative_passages.text: interaction between mathematical structures
negative_passages.docid: 35961
negative_passages.text: In what sense of "structure" do group homomorphisms "preserve structure"?
negative_passages.docid: 127691
negative_passages.text: Confusion Regarding Munkres's Definition of Basis for a Topology
negative_passages.docid: 60383
negative_passages.text: What is the intuition for the point-set topology definition of continuity?
negative_passages.docid: 136158
negative_passages.text: $X$ has Indiscrete topology $\implies$ any subset of $X$ is connected