Proof of a theorem of Burke and Hodel on the cardinality of topological spaces
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- by Robert L. Blair PDF
- Proc. Amer. Math. Soc. 78 (1980), 449-450 Request permission
Abstract:
Techniques of Pol are used to give a direct proof of Burke and Hodel’s inequality $|X| \leqslant {2^{\Delta (X) \cdot {\text {psw}}(X)}}$, where $\Delta (X)$ is the discreteness character of the ${T_1}$ space X and ${\text {psw}}(X)$ is the point separating weight of X.References
- 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 418014, DOI 10.1090/S0002-9939-1976-0418014-0
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- R. Pol, Short proofs of two theorems on cardinality of topological spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 1245–1249 (English, with Russian summary). MR 383333
- V. I. Ponomarev, The cardinality of bicompacta satisfying the first axiom of countability, Dokl. Akad. Nauk SSSR 196 (1971), 296–298 (Russian). MR 0275365
- B. Šapirovskiĭ, Discrete subspaces of topological spaces. Weight, tightness and Suslin number, Dokl. Akad. Nauk SSSR 202 (1972), 779–782 (Russian). MR 0292012
Additional Information
- © Copyright 1980 American Mathematical Society
- 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