科研之友
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摘要
In this paper, it is shown that every compact Hausdorff K-space has countable tightness. This result gives a positive answer to a problem posed by Malykhin and Tironi ['Weakly Frechet-Urysohn and Pytkeev spaces', Topology Appl. 104 (2000), 181-190]. We show that a semitopological group G that is a K-space is first countable if and only if G is of point-countable type. It is proved that if a topological group G is a K-space and has a locally paracompact remainder in some Hausdorff compactification, then G is metrisable.
