Topologically maximal convergences, accessibility, and covering maps

Szymon Dolecki; Michel Pillot

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 4, page 371-384
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Dolecki, Szymon, and Pillot, Michel. "Topologically maximal convergences, accessibility, and covering maps." Mathematica Bohemica 123.4 (1998): 371-384. <http://eudml.org/doc/248310>.

@article{Dolecki1998,
abstract = {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.},
author = {Dolecki, Szymon, Pillot, Michel},
journal = {Mathematica Bohemica},
keywords = {sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology; accessibility; sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology},
language = {eng},
number = {4},
pages = {371-384},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Topologically maximal convergences, accessibility, and covering maps},
url = {http://eudml.org/doc/248310},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Dolecki, Szymon
AU - Pillot, Michel
TI - Topologically maximal convergences, accessibility, and covering maps
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 4
SP - 371
EP - 384
AB - 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.
LA - eng
KW - sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology; accessibility; sequence-covering; compact-covering; strong accessibility; pseudotopology; paratopology; pretopology
UR - http://eudml.org/doc/248310
ER -

References

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  17. F. Siwiec, 10.1016/0016-660X(71)90120-6, Gen. Topology Appl. 1 (1971), 143-154. (1971) Zbl0218.54016MR0288737DOI10.1016/0016-660X(71)90120-6
  18. F. Siwiec V. J. Mancuso, Relations among certain mappings and conditions for their equivalence, Gen. Topology Appl. 1 (1971), 34-41. (1971) MR0282347
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