A conjecture on compact Fréchet spaces

Author:
Hao Xuan Zhou

Journal:
Proc. Amer. Math. Soc. **89** (1983), 326-328

MSC:
Primary 54D30; Secondary 03E50, 54D55

MathSciNet review:
712645

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Abstract | References | Similar Articles | Additional Information

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

**[B]**Andrew J. Berner,*𝛽(𝑋) can be Fréchet*, Proc. Amer. Math. Soc.**80**(1980), no. 2, 367–373. MR**577776**, 10.1090/S0002-9939-1980-0577776-3**[BCM]**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**0097043**, 10.1090/S0002-9939-1958-0097043-2**[IN]**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**, 10.1016/0166-8641(80)90027-9**[K]***Handbook of mathematical logic*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR**0457132****[R]***Handbook of mathematical logic*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR**0457132****[T]**Yoshio Tanaka,*Some results on sequential spaces*, Bull. Tokyo Gakugei Univ. (4)**33**(1981), 1–10. MR**635491****[T]**-, private communication.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0712645-X

Keywords:
Fréchet spaces,
feebly compact

Article copyright:
© Copyright 1983
American Mathematical Society