General Topology¶
Engelking, R. (1989). General Topology. Heldermann.
Cited by¶
12 citations across 12 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
- Development (topology)
- First-countable space
- Gδ Set
- A subspace of a completely metrizable space is completely metrizable precisely when it is Gδ in the ambient space
This sourceEngelking states the Alexandrov theorem in its general form - a subspace of a completely metrizable space is completely metrizable exactly when it is a G-delta - without any separability assumption.
SupportedVerified against the source
- A subspace of a completely metrizable space is completely metrizable precisely when it is Gδ in the ambient space
- H-closed space
- Hedgehog Space
- Scattered Space
- Listed in the references but not attached to a specific claim.
- Semiregular space
- Totally disconnected space
- Wallman compactification
- Waraszkiewicz spiral
Verification¶
Does it exist? Confirmed. This work's ISBN resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 12 citations: 1 supported. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 1 other way.
Registry ID ref:de59238bdb82 · see in the full table