General Topology

Willard, S. (2004). General Topology. Dover.

Type

Book

Intellectual base

Review or monograph

Year

2004

ISBN

9780486434797

Link

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

Cited from

mathematics

Cited by

13 citations across 13 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.
• Adherent point
  • … transfers from A canonical instance directly demonstrates that the topological space, subset and point are fixed and every neighborhood of the point has nonempty intersection with the subset. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• First-countable space
  • … the topological space and point, countable local family, neighborhood and open-set convention, refinement property at every neighborhood and any claimed sequential consequence are explicit. to An applied instance preserves the same invariant under changed scale, notation, dataset, jurisdiction, or implementation..
• Gδ Set
  • It is not necessarily closed, although every closed subset of a metrizable space is Gδ

    SupportedVerified against the source

    Read by an automated reader; not a human review. How support was checked

• Hausdorff Space
  • This is the \(T_2\) separation condition.
• Isolated point
  • … from A canonical instance directly demonstrates that ambient space, subset, point membership, topology or metric, and isolating neighborhood are explicit and exclude every other subset point. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Open Set
  • Point-set topology — the home turf, where the open sets are the topology: closed sets, continuity, convergence, compactness, connectedness, and the T₀–T₄ separation hierarchy are all defined in open-set terms.

    This sourceWillard's General Topology, whose contents and continuity discussion present convergence, compactness and the open-preimage definition of continuity as the book's subject matter.

    Supported in partVerified against the work's full text

    “and is represented here by sections on [convergence], [compactness], metrization and complete metric spaces”

    Read by an automated reader; not a human review. How support was checked

• Overlapping interval topology
  • … whole space, neighborhood systems, separation axioms compactness connectedness or countability properties used in the example and comparison with usual order and lower-limit topologies are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Positively separated sets
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• 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.
• Semiregular space
  • For example, the distinction between constitutive identity and a convenient observable transfers from Every regular topological space is semiregular because regular-open neighborhoods refine its topology. to A Hausdorff double-origin construction can be semiregular while failing regularity..
• Uniformizable space
  • A compatible uniformity supplies entourages that refine uniformly across the whole space and whose induced neighborhoods reproduce exactly the given topology.

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 2 of 13 citations: 1 supported, 1 supported in part. 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.

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Registry ID ref:001698065463 · see in the full table