General Topology

Willard, S. (1970). General Topology. Addison-Wesley.

Type

Book chapter

Intellectual base

Textbook

Year

1970

ISBN

9780486434797

Link

https://store.doverpublications.com/products/9780486434797

Cited from

mathematics

Cited by

8 citations across 8 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Topology
  • … the Hausdorff neighbourhood axioms) — and as Willard (1970) systematises in his comprehensive general-topology treatment, the structural equivalence of these presentations is itself a foundational result of point-set topology that licenses the analyst to choose the most natural presentation for a given problem.

    This sourceComprehensive reference on point-set topology covering bases, subbases, closure operators, neighbourhood systems, and the equivalence of these axiomatic presentations of a topology.

Domain-specific

• A-paracompact Space
  • A-paracompact Space is a topological space in which every open cover has a locally finite refinement, without requiring that the refining family itself be open.
• Gδ Set
  • It is not necessarily closed, although every closed subset of a metrizable space is Gδ
• Hausdorff Space
  • This is the \(T_2\) separation condition.
• Pseudometric space
  • Many pseudometrics arise from a seminorm \(p\) by \(d(x,y)=p(x-y)\), from ignoring selected coordinates, or from comparing observable features rather than underlying objects.
• Topological property
  • … if it holds for Y. The scope is broad within that domain but bounded by the need for for every homeomorphism X to Y, the property holds for X if and only if it holds for Y. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Uniform property
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Uniformizable space
  • A compatible uniformity supplies entourages that refine uniformly across the whole space and whose induced neighborhoods reproduce exactly the given topology.

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