The attempt to classify the objects of this category (up to homeomorphism) by invariants has motivated areas of research, such as homotopy theory, homology theory, and K-theory etc.
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Bourbaki, Nicolas; Elements of Mathematics: General Topology, Addison-Wesley (1966).
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Bredon, Glen E., Topology and Geometry (Graduate Texts in Mathematics), Springer; 1st edition (October 17, 1997).
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In mathematics, the Arens–Fort space is a special example in the theory of topological spaces, named for Richard Friederich Arens and M. K. Fort, Jr.
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology.
In topology, a branch of mathematics, the Knaster–Kuratowski fan (also known as Cantor's leaky tent or Cantor's teepee depending on the presence or absence of the apex) is a connected topological space with the property that the removal of a single point makes it totally disconnected.
The resulting topological space, sometimes written Rl and called the Sorgenfrey line after Robert Sorgenfrey, often serves as a useful counterexample in general topology, like the Cantor set and the long line.
Countably generated space, a topological space in which the topology is determined by its countable subsets
Homotopy lifting property, in algebraic topology, a technical condition on a continuous function from a topological space E to another one, B designed to support the picture of E "above" B
Ambient isotopy (or h-isotopy), two subsets of a fixed topological space are ambient isotopic if there is a homeomorphism, isotopic to the identity map of the ambient space, which carries one subset to the other
Piecewise linear manifold, a topological space formed by gluing together flat spaces