Cantor-connectedness revisited

Robert Lowen

Commentationes Mathematicae Universitatis Carolinae (1992)

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

Abstract

top
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

top

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

top
  1. Arhangel'skii A., Wiegandt R., Connectedness and disconnectedness in topology, Gen. Topology Appl. 5 (1975), 9-33. (1975) MR0367920
  2. Banas J., Goebel K., Measures of Non-Compactness in Banach Spaces, Marcel Dekker, 1980. MR0591679
  3. Cantor G., Über unendliche, lineare punktmannigfaltigkeiten, Math. Ann. 21 (1883), 545-591. (1883) MR1510215
  4. Connell E.M., Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), 974-979. (1959) Zbl0163.17705MR0110093
  5. De Groot J., De Vries J., Van der Walt M., Almost fixed point theorems for the euclidean plane, Math. Centre Tracts 1 (1967). (1967) 
  6. Fort M.K., Essential and non-essential fixed points, Amer. J. Math. 72 (1950), 315-322. (1950) Zbl0036.13001MR0034573
  7. Herrlich H., Categorical topology 1971-1981, Gen. Topol. Rel. Mod. Analysis and Algebra, Proc. 5th Prague Top. Symp., pages 279-383, 1983. Zbl0502.54001MR0698425
  8. Herrlich H., Einführung in die Topologie, Heldermann Verlag, 1986. Zbl0628.54001MR0846211
  9. Isiwata T., Metrization of additive κ -metric spaces, Proc. Amer. Math. Soc. 100 (1987), 164-168. (1987) Zbl0612.54033MR0883422
  10. Klee V.L., Stability of the fixed point property, Colloq. Math. 8 (1961), 43-46. (1961) Zbl0101.15101MR0126261
  11. Kuratowski C., Sur les espaces complets, Fund. Math. 15 (1930), 301-309. (1930) 
  12. Lowen E., Lowen R., Quasitopos hulls of categories containing topological and metric objects, Cahiers Topol. Géom. Diff. 30 (1989), 213-228. (1989) Zbl0706.18002MR1029625
  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
  17. Mrowka S., Pervin W.J., On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446-449. (1964) Zbl0126.18301MR0161307
  18. Preuss G., E-zusammenhangende Raüme, Manuscripta Math. 3 (1970), 331-342. (1970) MR0282323
  19. Preuss G., Relative connectedness and disconnectedness in topological categories, Quaest. Math. 2 (1977), 297-306. (1977) MR0500841
  20. Preuss G., Connection properties in topological categories and related topics, Lecture Notes in Mathematics 719 (1979), 293-307. (1979) Zbl0411.18002MR0544654
  21. Sčepin E.V., On κ -metrizable spaces, Math. USSR Izv. 14 (1980), 407-440. (1980) 

NotesEmbed ?

top

You must be logged in to post comments.