query: All topologies on $X=\{ a,b \}$
positive_passages.docid: 21938
positive_passages.text: describing all possible topologies on a set
negative_passages.docid: 27899
negative_passages.text: Can we prove the existence of $A\cup B$ without the union axiom?
negative_passages.docid: 85870
negative_passages.text: Show this set is a base for some topology on $\mathbb{Z}$
negative_passages.docid: 78513
negative_passages.text: Show finite complement topology is, in fact, a topology
negative_passages.docid: 135025
negative_passages.text: Axiomatization of a Topology using the Boundary
negative_passages.docid: 105996
negative_passages.text: Topology of matrices
negative_passages.docid: 119312
negative_passages.text: Product and Box Topologies
negative_passages.docid: 108226
negative_passages.text: Are these bases for a topology?
negative_passages.docid: 106756
negative_passages.text: Union and Intersection of Sets $A_{i}$ and $B_{j}$
negative_passages.docid: 152465
negative_passages.text: Find the intersection of all $T_2$ topologies on an infinite set $X$
negative_passages.docid: 39010
negative_passages.text: Metrization of the cofinite topology
negative_passages.docid: 93623
negative_passages.text: Showing that every connected open set in a locally path connected space is path connected
negative_passages.docid: 125761
negative_passages.text: Is this proof for Theorem 16.4 Munkres Topology correct?
negative_passages.docid: 106298
negative_passages.text: Prove that some topology is not metrizable
negative_passages.docid: 59813
negative_passages.text: Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
negative_passages.docid: 18039
negative_passages.text: Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
negative_passages.docid: 89264
negative_passages.text: Connectedness in the Quotient Space