General Topology¶
Kelley, J. L. (1955). General Topology. Springer.
Cited by¶
8 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Topology
- Separation axioms layer above the basic three to refine the class of topologies of interest: \(T_0\) (Kolmogorov, points are topologically distinguishable), \(T_1\) (Fréchet, singletons are closed), \(T_2\) (Hausdorff, distinct points have disjoint neighbourhoods — the working assumption for almost all of analysis), \(T_3\) (regular), \(T_4\) (normal, the assumption that supports Urysohn's lemma and the Tietze extension theorem), and the metrisability axioms (Urysohn's metrisation theorem; Nagata-Smirnov-Bing) that determine when a topology arises from a metric, all developed canonically by Kelley (1955) in General Topology.
This sourceCanonical reference on point-set topology including the separation axioms ($T_0$ through $T_4$), Urysohn's lemma, the Tietze extension theorem, and the metrisation theorems.
- Separation axioms layer above the basic three to refine the class of topologies of interest: \(T_0\) (Kolmogorov, points are topologically distinguishable), \(T_1\) (Fréchet, singletons are closed), \(T_2\) (Hausdorff, distinct points have disjoint neighbourhoods — the working assumption for almost all of analysis), \(T_3\) (regular), \(T_4\) (normal, the assumption that supports Urysohn's lemma and the Tietze extension theorem), and the metrisability axioms (Urysohn's metrisation theorem; Nagata-Smirnov-Bing) that determine when a topology arises from a metric, all developed canonically by Kelley (1955) in General Topology.
Domain-specific¶
- Completely metrizable space
- Hausdorff Maximal Principle
- Pseudometric space
- Open balls still define a topology, although points at zero distance have exactly the same neighborhoods and cannot be topologically separated.
This sourceVan Nostrand. Reprint: Springer, 1975. ISBN 978-0-387-90125-1.
- Open balls still define a topology, although points at zero distance have exactly the same neighborhoods and cannot be topologically separated.
- Sorgenfrey plane
- Uniform space
- Uniformizable space
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? Not recorded. Neither this nor any other of the 8 citations of this work carries a recorded support check.
Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.
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.
Registry ID ref:cf7c6ad7dbe1 · see in the full table