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Keywords:
sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology; accessibility
sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology; accessibility
Summary:
Topologically maximal pretopologies, paratopologies and pseudotopologies are characterized in terms of various accessibility properties. Thanks to recent convergence-theoretic descriptions of miscellaneous quotient maps (in terms of topological, pretopological, paratopological and pseudotopological projections), the quotient characterizations of accessibility (in particular, those of G. T. Whyburn and F. Siwiec) are shown to be instances of a single general theorem. Convergence-theoretic characterizations of sequence-covering and compact-covering maps are used to refine various results on the relationship between covering and quotient maps (by A. V. Arhangeľskii, E. Michael, F. Siwies and V. J. Mancuso) by deducing them from a single theorem.
References:
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