Geodesic
An Ultrafilter Completion of a Nearness Space
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 13-22

Voir la notice de l'article provenant de la source Cambridge University Press

An ultrafilter completion is constructed for a nearness space. It is shown to preserve the Tl separation axiom. Characterizing conditions are given for it to be topological or for its topology to be compact. It is shown to have the simple extension topology and for a given Hausdorff space a compatible nearness structure is found for which its ultrafilter completion is homeomorphic to the Katetov H-closed extension.
DOI : 10.4153/CMB-1981-002-4
Mots-clés : 54-02, 54A05, 54B99, 54D99, 54E05, Nearness space, Ultrafilter Complete, Reflective Subcategory, H-closed 
Carlson, John W. An Ultrafilter Completion of a Nearness Space. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 13-22. doi: 10.4153/CMB-1981-002-4
@article{10_4153_CMB_1981_002_4,
     author = {Carlson, John W.},
     title = {An {Ultrafilter} {Completion} of a {Nearness} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {13--22},
     year = {1981},
     volume = {24},
     number = {1},
     doi = {10.4153/CMB-1981-002-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-002-4/}
}
TY  - JOUR
AU  - Carlson, John W.
TI  - An Ultrafilter Completion of a Nearness Space
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 13
EP  - 22
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-002-4/
DO  - 10.4153/CMB-1981-002-4
ID  - 10_4153_CMB_1981_002_4
ER  - 
%0 Journal Article
%A Carlson, John W.
%T An Ultrafilter Completion of a Nearness Space
%J Canadian mathematical bulletin
%D 1981
%P 13-22
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-002-4/
%R 10.4153/CMB-1981-002-4
%F 10_4153_CMB_1981_002_4

[1] 1. Banaschewski, B., Extensions of topological spaces, Can. Math. Bull. 7 (1962) 1-22. Google Scholar

[2] 2. Bentley, H. L., Nearness spaces and extensions of topological spaces, Studies in Topology, Stavrakas, N. and Allen, K., Ed., Academic Press, New York, (1962) 47-66. Google Scholar

[3] 3. Bentley, H. L. and Herrlich, H., Extensions of topological spaces, Topological Proc. Memphis State Univ. Conference, Marcel-Dekker. New York (1962) 120-184. Google Scholar

[4] 4. Bentley, H. L. and Herrlich, H. and Robertson, W. A., Convenient Categories for topologists, Commentations Math. Univ. Carolina. 17 (1962) 207-227. Google Scholar

[5] 5. Carlson, J. W., B-Completeness in nearness spaces, Gen. Top. Appl. 5 (1962) 263-268. Google Scholar

[6] 6. Carlson, J. W., Topological properties in nearness spaces, Gen. Top. Appl. to appear. Google Scholar

[7] 7. Herrlich, H., A concept of nearness, Gen. Top. Appl. 5 (1962) 191-212. Google Scholar

[8] 8. Herrlich, H., Topological structures, Mathematical Centre Tracts 52, Amsterdam, 1974. Google Scholar

[9] 9. Herrlich, H., Some topological theorems which fail to be true, preprint. Google Scholar

[10] 10. Hunsaker, W. N. and Sharma, P. L., Nearness structures compatible with a topological space, Arch. Math. 25 (1962) 172-177. Google Scholar

[11] 11. Katêtov, K. M., Uber H-abgeschlossene and bikompakte Raume, Casopis Pest. Mat. Rys. 69 (1962) 36-49. Google Scholar

[12] 12. Naimpally, S. A., Reflective functors via nearness, Fundamenta Mathematicae, to appear. Google Scholar

Cité par Sources :