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Lindelöf locales and ℕ-compactness

Published online by Cambridge University Press:  24 October 2008

J. Paseka
J. Paseka
Affiliation:
J. E. Purkyně University, Brno, Czechoslovakia
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Extract

In the theory of locales (pointless topologies) some lattice-theoretical properties of certain classes of locales (Lindelöf, paracompact locales) behave ‘better’ than in the case of topological spaces. In this context we show that a locale is localic ‘ℕ-compact’ if and only if it is 0-dimensional Lindelöf. This is an analogue of the theorem of Madden and Vermeer [9] that a locale possesses the localic version of real compactness if and only if it is Tychonoff Lindelöf. As a consequence, we offer a localic analogue of ℕ-compactification, which is exactly the 0-dimensional Lindelöf reflection.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 187 - 191
Copyright
Copyright © Cambridge Philosophical Society 1991

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