F-points in countably compact spaces

Angelo Bella, V. I. Malykhin

Abstract

Answering a question of A.V. Arhangel'skii, we show that any extremally disconnected subspace of a compact space with countable tightness is discrete.

Keywords

F-point; Extremal disconnectedness; Compact; Countably compact; Pseudocompact; Countable tightness

Subject classification

54A25; 54A10

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References

A. V. Arhangel'skii, Strong disconnectedness properties and remainders in compacti cations, Topology Appl. 107, 1-2 (2000), 3-12. https://doi.org/10.1016/S0166-8641(99)00101-7

A. V. Arhangel'skii and A. Bella, Countable fan-tightness versus countable tightness, Comm. Math. Univ. Carolinae 37, 3 (1996), 565-576.

A. Bella and V. I. Malykhin, Tightness and resolvability, Comm. Math. Univ. Carolinae 39, 1 (1998), 177-184.

E. K. van Dowen, Applications of maximal topologies, Topology Appl. 51 (1993), 125-140. https://doi.org/10.1016/0166-8641(93)90145-4

V. I. Malykhin, Countable spaces having no bicompacti cations of countable tightness, Soviet Math. Dokl. 13 (1972), 1407-1411.

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