Near compactness of ditopological texture spaces

Year 2015, Volume: 44 Issue: 2, 261 - 276, 01.04.2015

Lawrence M. Brown Muhammed M. Gohar

Abstract

The authors consider the notions of near compactness, near cocompactness, near stability, near costability and near dicompactness in the setting of ditopological texture spaces. In particular preservation of these
properties under surjective R-dimaps, co-R-dimaps and bi-R-dimaps
is investigated and non-trivial characterizations of near dicompactness
are given which generalize those for dicompactness. The notions of
semiregularization, semicoregularization and semibiregularization are
defined and used to give generalizations of Mrówka’s Theorem for near
compactness and near cocompactness, and of Tychonoff’s Theorem for
near compactness, near cocompactness and near dicompactness. Also,
results related to pseudo-open and pseudo-closed sets are presented.
Finally, examples are given of co-$T_{1}$ nearly dicompact ditopologies on
textures which are not nearly plain and an open question is posed.

Keywords

Texture, Ditopology, Near compactness, Near cocompactness, Near stability, Near costabiliy, Near dicompactness, R-dimaps, co-R-dimaps, Semiregularization, Semicoregularization, Semibiregularization, Tychonoff theorems

References

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