Properties of locally H-closed spaces
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- by Mike Girou PDF
- Proc. Amer. Math. Soc. 113 (1991), 287-295 Request permission
Abstract:
This paper investigates the properties of locally $H$-closed spaces with regard to extensions, subspaces, and functions. We solve the $H$-closed extension remainder problem by showing that a space is locally $H$-closed if and only if it has a $\theta$-closed remainder in some $H$-closed extension. In fact, an $H$-closed space is Urysohn iff every $H$-closed subspace is $\theta$-closed. We solve the locally $H$-closed subspace problem by giving a necessary and sufficient condition for a subspace of a locally $H$-closed space to be locally $H$-closed. In particular, an open subspace of a locally $H$-closed space is locally $H$-closed if and only if its boundary is a $\theta$-closed subspace of its closure. An $H$-closed space is shown to be compact if and only if every open subset is locally $H$-closed. A retract of a locally $H$-closed space is locally $H$-closed.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 287-295
- MSC: Primary 54D99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1047001-5
- MathSciNet review: 1047001