Cantor-connectedness revisited

Robert Lowen

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 525-532
  • ISSN: 0010-2628

Abstract

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Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of metric spaces.

How to cite

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Lowen, Robert. "Cantor-connectedness revisited." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 525-532. <http://eudml.org/doc/247379>.

@article{Lowen1992,
abstract = {Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of metric spaces.},
author = {Lowen, Robert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {connected; Cantor-connected; metric space; topological space; approach space; approach space; uniformly connected pseudometric space},
language = {eng},
number = {3},
pages = {525-532},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Cantor-connectedness revisited},
url = {http://eudml.org/doc/247379},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Lowen, Robert
TI - Cantor-connectedness revisited
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 525
EP - 532
AB - Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of metric spaces.
LA - eng
KW - connected; Cantor-connected; metric space; topological space; approach space; approach space; uniformly connected pseudometric space
UR - http://eudml.org/doc/247379
ER -

References

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  13. Lowen R., Kuratowski's measure of non-compactness revisited, Quarterly J. Math. Oxford 39 (1988), 235-254. (1988) Zbl0672.54025MR0947504
  14. Lowen R., Approach spaces : a common supercategory of TOP and MET, Math. Nachr. 141 (1989), 183-226. (1989) Zbl0676.54012MR1014427
  15. Lowen R., A topological category suited for approximation theory, J. Approximation Theory 56 (1989), 108-117. (1989) Zbl0675.41046MR0977878
  16. Marny T., On epireflective subcategories of topological categories, Gen. Topol. Appl. 10 (1979), 175-181. (1979) Zbl0415.54007MR0527843
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  21. Sčepin E.V., On κ -metrizable spaces, Math. USSR Izv. 14 (1980), 407-440. (1980) 

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