Pytkeev space

Template:Short descriptionIn mathematics, and especially topology, a Pytkeev space is a topological space that satisfies qualities more subtle than a convergence of a sequence. They are named after E. G. Pytkeev, who proved in 1983 that sequential spaces have this property.

Definitions

Let X be a topological space. For a subset S of X let S denote the closure of S. Then a point x is called a Pytkeev point if for every set A with Template:Nowrap, there is a countable $\pi$-net of infinite subsets of A. A Pytkeev space is a space in which every point is a Pytkeev point.

Examples

• Every sequential space is also a Pytkeev space. This is because, if Template:Nowrap then there exists a sequence {a_k} that converges to x. So take the countable π-net of infinite subsets of A to be Template:Nowrap}.
• If X is a Pytkeev space, then it is also a Weakly Fréchet–Urysohn space.

Further reading

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