query: Why Use Arbitrary Unions and Finite Intersections in Topology?
positive_passages.docid: 50966
positive_passages.text: In a topological space, why the intersection only has to be finite?
negative_passages.docid: 93147
negative_passages.text: Topological groups, why need them?
negative_passages.docid: 30022
negative_passages.text: Why use the double cover instead of the universal cover of $SO(2)$?
negative_passages.docid: 42913
negative_passages.text: Equivalence of the definition of the Subbasis of a Topology
negative_passages.docid: 114856
negative_passages.text: Universal property of initial topology
negative_passages.docid: 39010
negative_passages.text: Metrization of the cofinite topology
negative_passages.docid: 88205
negative_passages.text: How can I define a topology on the empty set?
negative_passages.docid: 133820
negative_passages.text: The product topology on $\mathbb R_d\times \mathbb R$ vs. the dictionary order topology on $\mathbb R\times \mathbb R$
negative_passages.docid: 128111
negative_passages.text: Why is a deductive closure an intersection of maximally consistent sets?
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure
negative_passages.docid: 139988
negative_passages.text: Counter example for a result of intersection of subspaces
negative_passages.docid: 77563
negative_passages.text: Homeomorphism between spaces equipped with cofinite topologies
negative_passages.docid: 130156
negative_passages.text: Image of the union and intersection of sets.
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 79213
negative_passages.text: Proof about a Topological space being arc connect
negative_passages.docid: 46121
negative_passages.text: Does the intersection of two finite index subgroups have finite index?
negative_passages.docid: 137075
negative_passages.text: If a topology contains all infinite subsets, then it is the discrete topology