Continuum neighborhoods and filterbases
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- by David P. Bellamy and Harvey S. Davis PDF
- Proc. Amer. Math. Soc. 27 (1971), 371-374 Request permission
Abstract:
In this paper we prove that if $\Gamma$ is a filterbase of closed subsets of a compact Hausdorff space then $T( \bigcap \Gamma ) = \bigcap \{ T(G)|G \in \Gamma \}$, where $T(A)$ denotes the set of those points for which every neighborhood which is a continuum intersects $A$ nonvoidly.References
- H. S. Davis, D. P. Stadtlander, and P. M. Swingle, Properties of the set functions $T^{n}$, Portugal. Math. 21 (1962), 113–133. MR 142108
- H. S. Davis, A note on connectedness im kleinen, Proc. Amer. Math. Soc. 19 (1968), 1237–1241. MR 254814, DOI 10.1090/S0002-9939-1968-0254814-3
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 371-374
- MSC: Primary 54.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276913-2
- MathSciNet review: 0276913