| Title:
|
Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set (English) |
| Author:
|
Alas, Ofelia T. |
| Author:
|
Wilson, Richard G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
641-652 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_1$-topologies on a set $X$. (English) |
| Keyword:
|
KC-space |
| Keyword:
|
$T_1$-complementary topology |
| Keyword:
|
$T_1$-independent |
| Keyword:
|
sequential space |
| MSC:
|
54A10 |
| MSC:
|
54D10 |
| MSC:
|
54D25 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1090.54015 |
| idMR:
|
MR2045786 |
| . |
| Date available:
|
2009-01-08T19:25:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119353 |
| . |
| Reference:
|
[1] Anderson B.A.: A class of topologies with $T_1$-complements.Fund. Math. 69 (1970), 267-277. MR 0281140 |
| Reference:
|
[2] Anderson B.A., Stewart D.G.: $T_1$-complements of $T_1$-topologies.Proc. Amer. Math. Soc. 23 (1969), 77-81. MR 0244927 |
| Reference:
|
[3] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[4] Fleissner W.G.: A $T_B$-space which is not Katětov $T_B$.Rocky Mountain J. Math. 10 3 (1980), 661-663. Zbl 0448.54021, MR 0590229 |
| Reference:
|
[5] Franklin S.P.: Spaces in which sequences suffice.Fund. Math. 57 (1965), 107-115. Zbl 0132.17802, MR 0180954 |
| Reference:
|
[6] Pelant J., Tkačenko M.G., Tkachuk V.V., Wilson R.G.: Pseudocompact Whyburn spaces need not be Fréchet.submitted. |
| Reference:
|
[7] Shakhmatov D., Tkačenko M.G., Wilson R.G.: Transversal and $T_1$-independent topologies.submitted. |
| Reference:
|
[8] Simon P.: On accumulation points.Cahiers Topologie Géom. Différentielle Catégoriques 35 (1994), 321-327. Zbl 0858.54008, MR 1307264 |
| Reference:
|
[9] Smythe N., Wilkins C.A.: Minimal Hausdorff and maximal compact spaces.J. Austral. Math. Soc. 3 (1963), 167-177. Zbl 0163.17201, MR 0154254 |
| Reference:
|
[10] Steen L.A., Seebach J.A.: Counterexamples in Topology.Second Edition, Springer Verlag, New York, 1978. Zbl 0386.54001, MR 0507446 |
| Reference:
|
[11] Steiner A.K.: Complementation in the lattice of $T_1$-topologies.Proc. Amer. Math. Soc. 17 (1966), 884-885. MR 0193033 |
| Reference:
|
[12] Steiner E.F., Steiner A.K.: Topologies with $T_1$-complements.Fund. Math. 61 (1967), 23-28. MR 0230277 |
| Reference:
|
[13] Tkačenko M.G., Tkachuk V.V., Wilson R.G., Yaschenko I.V.: No submaximal topology on a countable set is $T_1$-complementary.Proc. Amer. Math. Soc. 128 1 (1999), 287-297. MR 1616605 |
| Reference:
|
[14] Wilansky A.: Between $T_1$ and $T_2$.Amer. Math. Monthly 74 (1967), 261-266. MR 0208557 |
| . |
