query: Homeomorphism of topological spaces.
positive_passages.docid: 157987
positive_passages.text: Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?
negative_passages.docid: 103397
negative_passages.text: Homeomorphisms between infinite-dimensional Banach spaces and their spheres
negative_passages.docid: 48557
negative_passages.text: Product of connected spaces
negative_passages.docid: 46563
negative_passages.text: Show that the quotient space is homeomorphic to the n-disc
negative_passages.docid: 144246
negative_passages.text: Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
negative_passages.docid: 70049
negative_passages.text: Irreducible topological spaces and irreducible Hausdorff space
negative_passages.docid: 79213
negative_passages.text: Proof about a Topological space being arc connect
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 160
negative_passages.text: homeomorphism non-example
negative_passages.docid: 103717
negative_passages.text: Topological Property of the Set of Integers
negative_passages.docid: 120685
negative_passages.text: Topology induced from Kuratowski Closure properties
negative_passages.docid: 34699
negative_passages.text: A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism
negative_passages.docid: 148112
negative_passages.text: Prove that a topological space equipped with a delta-complex structure is Hausdorff
negative_passages.docid: 20547
negative_passages.text: Homeomorphism that maps given points to given points
negative_passages.docid: 154324
negative_passages.text: preservation of completeness under homeomorphism
negative_passages.docid: 144383
negative_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 18034
negative_passages.text: Is there an equivalence relation of which the quotient topology is homeomorphic to codomain of a quotient map?