A conjecture on compact Fréchet spaces

A conjecture on compact Fréchet spaces
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by Hao Xuan Zhou PDF

Proc. Amer. Math. Soc. 89 (1983), 326-328 Request permission

Let $X$ be a compact Hausdorff space. $X$ is Fréchet if every feebly compact subset is closed in $X$. Under MA, the converse is false.

References

Andrew J. Berner, $\beta (X)$ can be Fréchet, Proc. Amer. Math. Soc. 80 (1980), no. 2, 367–373. MR 577776, DOI 10.1090/S0002-9939-1980-0577776-3
R. W. Bagley, E. H. Connell, and J. D. McKnight Jr., On properties characterizing pseudo-compact spaces, Proc. Amer. Math. Soc. 9 (1958), 500–506. MR 97043, DOI 10.1090/S0002-9939-1958-0097043-2
Mohammad Ismail and Peter Nyikos, On spaces in which countably compact sets are closed, and hereditary properties, Topology Appl. 11 (1980), no. 3, 281–292. MR 585273, DOI 10.1016/0166-8641(80)90027-9
Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132
Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132
Yoshio Tanaka, Some results on sequential spaces, Bull. Tokyo Gakugei Univ. (4) 33 (1981), 1–10. MR 635491