weakly countably compact

A topological space $X$ is said to be weakly countably compact(or limit point compact)if every infinite subset of $X$ has a limit point.

Every countably compact space is weakly countably compact.The converse is true in $\\mathrm{T}_{1}$ spaces (http://planetmath.org/T1Space).

A metric space is weakly countably compact if and only if it is compact.

An easy example of a space $X$ that is not weakly countably compactis any infinite set with the discrete topology.A more interesting example is the countable complement topologyon an uncountable set.

单词	WeaklyCountablyCompact
释义	weakly countably compact A topological space $X$ is said to be weakly countably compact(or limit point compact)if every infinite subset of $X$ has a limit point. Every countably compact space is weakly countably compact.The converse is true in $\\mathrm{T}_{1}$ spaces (http://planetmath.org/T1Space). A metric space is weakly countably compact if and only if it is compact. An easy example of a space $X$ that is not weakly countably compactis any infinite set with the discrete topology.A more interesting example is the countable complement topologyon an uncountable set.
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