General Topology¶
Engelking, R. (1989). General Topology. Heldermann Verlag.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Closure
- Continuous functions between topological spaces are characterised by their preservation of the closure operator (a function \(f: X \to Y\) is continuous if and only if \(f(\overline{S}) \subseteq \overline{f(S)}\) for every \(S \subseteq X\)), and the closure-operator framework gives the cleanest abstract definition of continuity in the category-theoretic treatment of topology, an equivalence Engelking (1989) treats systematically in General Topology.
This sourceComprehensive general-topology reference systematically developing closure operators, the equivalence between continuity and closure-preservation, and the categorical-topological framework.
- Continuous functions between topological spaces are characterised by their preservation of the closure operator (a function \(f: X \to Y\) is continuous if and only if \(f(\overline{S}) \subseteq \overline{f(S)}\) for every \(S \subseteq X\)), and the closure-operator framework gives the cleanest abstract definition of continuity in the category-theoretic treatment of topology, an equivalence Engelking (1989) treats systematically in General Topology.
Domain-specific¶
- Collectionwise Normal Space
- First-countable space
- Hedgehog Space
- Scattered Space
- Listed in the references but not attached to a specific claim.
- Semiregular space
- Totally disconnected space
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