query: homeomorphism between a compact and a Hausdorff space
positive_passages.docid: 148403
positive_passages.text: Compact space and Hausdorff space
negative_passages.docid: 31479
negative_passages.text: homeomorphism of cantor set extends to the plane?
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
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: 115794
negative_passages.text: When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
negative_passages.docid: 149426
negative_passages.text: Is there a Hausdorff space $X$ separating points of any Hausdorff space?
negative_passages.docid: 100121
negative_passages.text: Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
negative_passages.docid: 71916
negative_passages.text: Quasi-components and components coincide for compact Hausdorff spaces
negative_passages.docid: 46970
negative_passages.text: If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
negative_passages.docid: 149220
negative_passages.text: If every compact set is closed, then is the space Hausdorff?
negative_passages.docid: 37654
negative_passages.text: Topology: Example of a compact set but its closure not compact
negative_passages.docid: 118045
negative_passages.text: Is the Baire space $\sigma$-compact?
negative_passages.docid: 70049
negative_passages.text: Irreducible topological spaces and irreducible Hausdorff space
negative_passages.docid: 14509
negative_passages.text: Contraction Map on Compact Normed Space has a Fixed Point
negative_passages.docid: 148187
negative_passages.text: Question regarding one-point compactification and homeomorphisms
negative_passages.docid: 143269
negative_passages.text: Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$
negative_passages.docid: 149980
negative_passages.text: Are there any countable Hausdorff connected spaces?