Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set
Alas, Ofelia Teresa ; Wilson, Richard Gordon
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 641-652 / Harvested from Czech Digital Mathematics Library
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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 $X$.

Publié le : 2002-01-01
Classification:  54A10,  54D10,  54D25,  54D55 
@article{119353,
     author = {Ofelia Teresa Alas and Richard Gordon Wilson},
     title = {Spaces in which compact subsets are closed and the lattice of $T\_1$-topologies on a set},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {641-652},
     zbl = {1090.54015},
     mrnumber = {2045786},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119353}
}

Alas, Ofelia Teresa; Wilson, Richard Gordon. Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 641-652. http://gdmltest.u-ga.fr/item/119353/

Anderson B.A. A class of topologies with $T_1$-complements, Fund. Math. 69 (1970), 267-277. (1970) | MR 0281140

Anderson B.A.; Stewart D.G. $T_1$-complements of $T_1$-topologies, Proc. Amer. Math. Soc. 23 (1969), 77-81. (1969) | MR 0244927

Engelking R. General Topology, Heldermann Verlag, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

Fleissner W.G. A $T_B$-space which is not Katětov $T_B$, Rocky Mountain J. Math. 10 3 (1980), 661-663. (1980) | MR 0590229 | Zbl 0448.54021

Franklin S.P. Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115. (1965) | MR 0180954 | Zbl 0132.17802

Pelant J.; Tkačenko M.G.; Tkachuk V.V.; Wilson R.G. Pseudocompact Whyburn spaces need not be Fréchet, submitted.

Shakhmatov D.; Tkačenko M.G.; Wilson R.G. Transversal and $T_1$-independent topologies, submitted.

Simon P. On accumulation points, Cahiers Topologie Géom. Différentielle Catégoriques 35 (1994), 321-327. (1994) | MR 1307264 | Zbl 0858.54008

Smythe N.; Wilkins C.A. Minimal Hausdorff and maximal compact spaces, J. Austral. Math. Soc. 3 (1963), 167-177. (1963) | MR 0154254 | Zbl 0163.17201

Steen L.A.; Seebach J.A. Counterexamples in Topology, Second Edition, Springer Verlag, New York, 1978. | MR 0507446 | Zbl 0386.54001

Steiner A.K. Complementation in the lattice of $T_1$-topologies, Proc. Amer. Math. Soc. 17 (1966), 884-885. (1966) | MR 0193033

Steiner E.F.; Steiner A.K. Topologies with $T_1$-complements, Fund. Math. 61 (1967), 23-28. (1967) | MR 0230277

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. (1999) | MR 1616605

Wilansky A. Between $T_1$ and $T_2$, Amer. Math. Monthly 74 (1967), 261-266. (1967) | MR 0208557