Measures of compactness in approach spaces

R. Baekeland; Robert Lowen

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 327-345
  • ISSN: 0010-2628

Abstract

top
We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.

How to cite

top

Baekeland, R., and Lowen, Robert. "Measures of compactness in approach spaces." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 327-345. <http://eudml.org/doc/247729>.

@article{Baekeland1995,
abstract = {We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.},
author = {Baekeland, R., Lowen, Robert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approach space; compactness; approach space; measure of relative compactness; measure of compactness},
language = {eng},
number = {2},
pages = {327-345},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Measures of compactness in approach spaces},
url = {http://eudml.org/doc/247729},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Baekeland, R.
AU - Lowen, Robert
TI - Measures of compactness in approach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 327
EP - 345
AB - We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.
LA - eng
KW - approach space; compactness; approach space; measure of relative compactness; measure of compactness
UR - http://eudml.org/doc/247729
ER -

References

top
  1. Baekeland R., Lowen R., Measures of Lindelöf and separability in approach spaces, to appear in Internat. J. Math & Math. Sci. Zbl0813.54022MR1277744
  2. Beer G., On a measure of non-compactness, Rend. Mat. Appl. 72 (1987), 193-205 (1988). (1987) 
  3. Bourbaki N., Elements de Mathématique : Livre III, Topologie générale', Hermann, Paris, 1962. Zbl0305.54003
  4. Dugundji J., Topology, Allan and Bacon, Boston, 1966. Zbl0397.54003MR0193606
  5. Gaal S., Point Set Topology, Academic Press, New York, 1964. Zbl0124.15401MR0171253
  6. Lowen E., Lowen R., A quasi-topos containing CONV and MET as full subcategories, Internat. J. Math. & Math. Sci. 11:3 (1988), 417-438. (1988) MR0947271
  7. Lowen E., Lowen R., Topological quasitopos hulls of categories containing topological and metric objects, Cahiers de Topologie et Géométrie différentielle catégoriques 30:3 (1989), 213-228. (1989) Zbl0706.18002MR1029625
  8. Lowen R., Approach spaces: a common supercategory of TOP and MET, Math. Nachr. 141 (1989), 183-226. (1989) Zbl0676.54012MR1014427
  9. Lowen R., Kuratowski's measure of non-compactness revisited, Quart. J. Math. Oxford 39:2 (1988), 235-254. (1988) Zbl0672.54025MR0947504
  10. Lowen R., Robeys K., Completion of products of metric spaces, Quart. J. Math. Oxford 43:2 (1992), 319-338. (1992) MR1176491
  11. Kuratowski C., Sur les espaces complets, Fund. Math. 15 (1930), 301-309. (1930) 
  12. Steen L.A., Seebach J.A., Jr., Counterexamples in Topology, Holt, Rinehart and Winston, Inc, 1970. Zbl0386.54001MR0266131
  13. Thron W.J., Topological Structures, Holt, Rinehart and Winston, 1966. Zbl0137.15402MR0200892
  14. Wilansky A., Topology for Analysis, Ginn, Waltham, Massachusetts, Toronto, London, 1970. Zbl0512.54001MR0451181
  15. Willard S., General Topology, Addison-Wesley Series in Mathematics, Reading, Massachusetts, 1970. Zbl1052.54001MR0264581

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.