Spaces in which compact subsets are closed and the lattice of T1T_1-topologies on a set

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 $X$

Which topologies can have immediate successors in the lattice of T1-topologies?

[EN] We give a new characterization of those topologies which have an immediate successor or cover in the lattice of T1-topologies on a set and show that certain classes of compact and countably compact topologies do not have covers.Research supported by Consejo Nacional de Ciencia y Tecnología (México), grant 38164-E and Fundacão de Amparo a Pesquisa do Estado de São Paulo (Brasil)Alas, OT.; Wilson, RG. (2004). Which topologies can have immediate successors in the lattice of T1-topologies?. Applied General Topology. 5(2):231-242. doi:10.4995/agt.2004.1972.SWORD2312425

The Cech number of Cp(X) when X is an ordinal space

[EN] The Cech number of a space Z, C(Z), is the pseudocharacter of Z in βZ. In this article we obtain, in ZFC and assuming SCH, some upper and lower bounds of the Cech number of spaces Cp(X) of realvalued continuous functions defined on an ordinal space X with the pointwise convergence topologyResearch supported by Fapesp, CONACyT and UNAM.Alas, OT.; Tamariz-Mascarúa, Á. (2008). The Cech number of Cp(X) when X is an ordinal space. Applied General Topology. 9(1):67-76. doi:10.4995/agt.2008.1870.SWORD67769

On countably compact product spaces

Si studiano in ZF forme equivalenti della seguente versione debole del teorema di Tychonov: il prodotto topologico di spazi compatti di Hausdoff è numerabilmente compatto.We study in ZF equivalent forms of the following weaker version of Tychonov theorem: the topological product of compact Hausdorff spaces is countably compact

The structure of the poset of regular topologies on a set

We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E3. We also consider the problem of when an R-closed topology is maximal R-closed

Correction to: Some results and examples concerning Whyburn spaces

[EN] We correct the proof of Theorem 2.9 of the paper mentioned in the title (published in Applied General Topology, 13 No.1 (2012), 11-19).Alas, OT.; Madriz-Mendoza, M.; Wilson, RG. (2012). Correction to: Some results and examples concerning Whyburn spaces. Applied General Topology. 13(2):225-226. doi:10.4995/agt.2012.1631.SWORD22522613

Some results and examples concerning Whyburn spaces

[EN] We prove some cardinal inequalities valid in the classes of Whyburn and hereditarily weakly Whyburn spaces and we construct examples of non-Whyburn and non-weakly Whyburn spaces to illustrate that some previously known results cannot be generalized.This research was supported by the network Algebra, Topolog´ıa y An´alisis del PROMEP, Project 12611243 (México) and Fundação de Amparo a Pesquisa do Estado de São Paulo (Brasil). The third author wishes to thank the Departament de Matemàtiques de la Universitat Jaume I for support from Pla 2009 de Promoció de la Investigació, Fundació Bancaixa, Castelló, while working on an early draft of this article.Alas, OT.; Madriz-Mendoza, M.; Wilson, RG. (2012). Some results and examples concerning Whyburn spaces. Applied General Topology. 13(1):11-19. https://doi.org/10.4995/agt.2012.1633SWORD111913