General Topology

Topological spaces, continuity, compactness, connectedness, and separation axioms.

foundation tier

General Topology. Topological spaces, continuity, compactness, connectedness, and separation axioms. This page collects canonical references that organise the subject and provide entry points to its main techniques.

Foundations and canonical references

The standard treatments of general topology approach the subject from complementary angles. Munkres, Topology (2000) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Kelley, General Topology (1975) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for general topology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2000
    Topology
    munkres-2000
  • textbook · primary · 1975
    General Topology
    kelley-1975

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Explore

  1. 01

    Metrization and Uniform Spaces

    Urysohn, Nagata–Smirnov, and uniform structures.
  2. 02

    Continuum Theory

    Topology of compact connected metric spaces and indecomposable continua.
  3. 03

    Descriptive Set Theory

    Borel and analytic sets, Polish spaces, and definability hierarchies.

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