Proof of a theorem of Burke and Hodel on the cardinality of topological spaces

Author:
Robert L. Blair

Journal:
Proc. Amer. Math. Soc. **78** (1980), 449-450

MSC:
Primary 54A25

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553393-6

MathSciNet review:
553393

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Abstract | References | Similar Articles | Additional Information

Abstract: Techniques of Pol are used to give a direct proof of Burke and Hodel's inequality , where is the discreteness character of the space *X* and is the point separating weight of *X*.

**[BH]**D. K. Burke and R. E. Hodel,*The number of compact subsets of a topological space*, Proc. Amer. Math. Soc.**58**(1976), 363-368. MR**0418014 (54:6058)****[E]**R. Engelking,*General topology*, PWN, Warsaw, 1975; English Transl., PWN, Warsaw, 1977. MR**0500780 (58:18316b)****[P]**R. Pol,*Short proof of two theorems on cardinality of topological spaces*, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.**22**(1974), 1245-1249. MR**0383333 (52:4214)****[P]**V. I. Ponomarev,*On the cardinality of bicompacta which satisfy the first axiom of countability*, Dokl. Akad. Nauk SSSR**196**(1971), 296-298 = Soviet Math. Dokl.**12**(1971), 121-124. MR**0275365 (43:1122)****[S]**B. Šapirovskiĭ,*On discrete subspaces of topological spaces*:*weight, tightness and Suslin number*, Dokl. Akad. Nauk SSSR**202**(1972), 779-782 = Soviet Math. Dokl.**13**(1972), 215-219. MR**0292012 (45:1100)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553393-6

Keywords:
Cardinality of a topological space,
separating open cover,
point separating weight,
discreteness character

Article copyright:
© Copyright 1980
American Mathematical Society