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Compactifications and A-compactifications of frames. Proximal frames

Published online by Cambridge University Press:  24 October 2008

Georgi D. Dimov  and
Gino Tironi
Georgi D. Dimov
Affiliation:
Department of Mathematics and Computer Science, University ofSofia, Blvd. J. Bourchier 5.1126 Sofia, Bulgaria
Gino Tironi
Affiliation:
Department of Mathematical Sciences, University of Trieste, P.le Europa 1, 34100 Trieste, Italy
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Extract

The aim of this paper is to give two new descriptions of the ordered set of all (up to equivalence) regular compactifications of a completely regular frame. F and to introduce and study the notion of A-frame as a generalization of the notion of Alexandroff space (known also as zero-set space) (Alexandroff[l], Gordon[15]). A description of the ordered set of all (up to equivalence) A-compactifications of an A-frame by means of an ordered by inclusion set of some distributive lattices (called AP-sublattices) is obtained. It implies that any A-frame has a greatest A-compactification and leads to the descriptions of A new category isomorphic to the category of proximal frames is introduced. A question for compactifications of frames analogous to the R. Chandler's question [8, p. 71] for compactifications of spaces is formulated and solved. Many results of [1], [3], [15], [23], [9], [10] and [11] are generalized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 2 , February 1996 , pp. 321 - 339
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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