A note on functionally compact spaces

Bella, Angelo

doi:10.1090/S0002-9939-1986-0857951-6

A note on functionally compact spaces
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by Angelo Bella PDF

Proc. Amer. Math. Soc. 98 (1986), 507-512 Request permission

Abstract:

In this paper we give some characterizations of functionally compact Hausdorff spaces in terms of multifunctions. Also, some applications are presented.

References

Jesse P. Clay and James E. Joseph, A characterization of $C$-compact spaces, Proc. Amer. Math. Soc. 82 (1981), no. 4, 657–658. MR 614899, DOI 10.1090/S0002-9939-1981-0614899-5
R. F. Dickman Jr. and A. Zame, Functionally compact spaces, Pacific J. Math. 31 (1969), 303–311. MR 259860
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
L. L. Herrington, Characterizations of functionally compact spaces, J. Austral. Math. Soc. Ser. A 29 (1980), no. 1, 71–79. MR 566277
G. Goss and G. Viglino, Some topological properties weaker than compactness, Pacific J. Math. 35 (1970), 635–638. MR 279770
Larry L. Herrington and Paul E. Long, Characterizations of $C$-compact spaces, Proc. Amer. Math. Soc. 52 (1975), 417–426. MR 388345, DOI 10.1090/S0002-9939-1975-0388345-0

Separation properties and

-compact spaces

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Teck Cheong Lim and Kok Keong Tan, Functional compactness and $C$-compactness, J. London Math. Soc. (2) 9 (1974/75), 371–377. MR 355968, DOI 10.1112/jlms/s2-9.2.371
R. E. Smithson, Multifunctions, Nieuw Arch. Wisk. (3) 20 (1972), 31–53. MR 305338
Giovanni Viglino, $C$-compact spaces, Duke Math. J. 36 (1969), 761–764. MR 248749
Giovanni Viglino, Seminormal and $C$-compact spaces, Duke Math. J. 38 (1971), 57–61. MR 271908
A. Bella and F. Cammaroto, On the cardinality of Urysohn spaces, Canad. Math. Bull. 31 (1988), no. 2, 153–158. MR 942065, DOI 10.4153/CMB-1988-023-4
Szymon Dolecki and Alojzy Lechicki, On structure of upper semicontinuity, J. Math. Anal. Appl. 88 (1982), no. 2, 547–554. MR 667078, DOI 10.1016/0022-247X(82)90213-X
Szymon Dolecki and Stefan Rolewicz, Metric characterizations of upper semicontinuity, J. Math. Anal. Appl. 69 (1979), no. 1, 146–152. MR 535287, DOI 10.1016/0022-247X(79)90184-7