query: Counterxample: A continuous closed surjective map doesn't preserve Hausdorff property
positive_passages.docid: 20437
positive_passages.text: Closed surjection that does not preserve regularity
negative_passages.docid: 32340
negative_passages.text: Continuous bijections and their inverses
negative_passages.docid: 14282
negative_passages.text: $X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$
negative_passages.docid: 154324
negative_passages.text: preservation of completeness under homeomorphism
negative_passages.docid: 158523
negative_passages.text: Topology: Proof that a finitely generated cone is closed
negative_passages.docid: 4538
negative_passages.text: Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
negative_passages.docid: 70785
negative_passages.text: A finite Hausdorff space is discrete
negative_passages.docid: 110885
negative_passages.text: Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
negative_passages.docid: 111689
negative_passages.text: Surjective, but not injective endomorphism
negative_passages.docid: 71916
negative_passages.text: Quasi-components and components coincide for compact Hausdorff spaces
negative_passages.docid: 20284
negative_passages.text: Continuous injective map is strictly monotonic
negative_passages.docid: 132571
negative_passages.text: Local homeomorphisms which are not covering map?
negative_passages.docid: 70645
negative_passages.text: Borel set preserved by continuous map
negative_passages.docid: 136538
negative_passages.text: How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
negative_passages.docid: 94165
negative_passages.text: Why is a map to a smaller dimensional space not injective?
negative_passages.docid: 143043
negative_passages.text: When is a local homeomorphism a covering map?
negative_passages.docid: 16610
negative_passages.text: Surjectivity of a map from a space to itself