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

top
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

top

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

top
  1. A. V. Arhangeľskii, Some types of factor mappings and the relations between classes of topological spaces, Dokl. Akad. Nauk SSSR 153 (1963), 743-763. (1963) MR0158362
  2. A. V. Arhangeľskii, On quotient mappings defined on metric spaces, Soviet Math. Dokl. 5 (1964), 368-371. (1964) 
  3. G. Choquet, Convergences, Ann. Univ. Grenoble 23 (1947-48), 55-112. (1947) MR0025716
  4. S. Dolecki, 10.1016/0166-8641(96)00067-3, Topology Appl. 73 (1996). 1-21. (1996) MR1413721DOI10.1016/0166-8641(96)00067-3
  5. S. Dolecki G. H. Greco, 10.4064/sm-77-3-265-281, Studia Math. 77 (1984), 265-281. (1984) MR0745283DOI10.4064/sm-77-3-265-281
  6. S. Dolecki G. H. Greco, 10.1002/mana.19861270123, Math. Nachr. 127 (1986), 317-334. (1986) MR0861735DOI10.1002/mana.19861270123
  7. R. Engelking, Topology, PWN, 1977. (1977) Zbl0373.54002
  8. S. Franklin, 10.4064/fm-57-1-107-115, Fund. Math. 57 (1965), 107-115. (1965) Zbl0132.17802MR0180954DOI10.4064/fm-57-1-107-115
  9. S. Franklin, 10.4064/fm-61-1-51-56, Fund. Math. 61 (1967), 51-56. (1967) Zbl0168.43502MR0222832DOI10.4064/fm-61-1-51-56
  10. W. Gähler, Grundstrukturen der Analysis, Akademie-Verlag, 1977. (1977) MR0459969
  11. O. Hájek, Notes on quotient maps, Comment. Math. Univ. Carolin. 7(1966), 319-323. (1966) MR0202118
  12. V. Kannan, 10.1090/memo/0245, Memoirs Amer. Math. Soc. 32 (1981), no. 245, 1-164. (1981) Zbl0473.54001MR0617500DOI10.1090/memo/0245
  13. D. C. Kent, 10.4064/fm-65-2-197-205, Fund. Math. 65 (1969), 197-205. (1969) Zbl0179.51002MR0250258DOI10.4064/fm-65-2-197-205
  14. E. Michael, 10.5802/aif.301, Ann. Inst. Fourier (Grenoble) 18 (1968), 287-302. (1968) Zbl0175.19704MR0244964DOI10.5802/aif.301
  15. E. Michael, N 0 -spaces, J. Math. Mech. 15 (1966), 983-1002. (1966) MR0206907
  16. E. Michael, 10.1016/0016-660X(72)90040-2, Gen. Topology Appl. 2 (1972), 91-138. (1972) Zbl0238.54009MR0309045DOI10.1016/0016-660X(72)90040-2
  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
  19. G. T. Whyburn, 10.1215/S0012-7094-56-02321-3, Duke Math. J. 23 (1956), 237-240. (1956) Zbl0071.38201MR0098361DOI10.1215/S0012-7094-56-02321-3
  20. G. T Whyburn, 10.1090/S0002-9939-1970-0248722-0, Proc. Amer. Math. Soc. 24 (1970), 181-185. (1970) Zbl0197.48602MR0248722DOI10.1090/S0002-9939-1970-0248722-0

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.