Topological spaces with point-networks
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- by Zoltán T. Balogh PDF
- Proc. Amer. Math. Soc. 94 (1985), 497-501 Request permission
Abstract:
In this paper we introduce the notion of a point-network and prove that in ${T_1}$ spaces having a point-network, countable pseudocharacter implies stratifiable. As a corollary, there follows Reed’s theorem that a ${T_1}$ space is metrizable if and only if it has an open point-network.References
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- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779 G. M. Reed, Handwritten notes, October 1983.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 497-501
- MSC: Primary 54E20; Secondary 54D18, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787901-1
- MathSciNet review: 787901