We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under...
Si stabilisce un'estensione di un teorema di Blumberg includente altre più o meno recenti estensioni [4, 5, 2].
Si stabiliscono proprietà di due invarianti topologici riferiti, rispettivamente, alla intersezione di una collezione d'insiemi aperti ed ai ricoprimenti aperti localmente finiti di uno spazio.
Relazione tra un tipo particolare di prodotto di spazi topologici e le funzioni -continue. Dimostrazione di un risultato generalizzante un teorema di A.M. Gleason.
Si assegnano condizioni atte ad assicurare la metrizzabilità di uno spazio di Hausdorff.
For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have...
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 -topologies on a set .
A in a space is a family of open subsets of such that for any . A set is if . If every neighbourhood assignment in has a closed and discrete (respectively, discrete) kernel, then is said to be a -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf -space is a -space and we prove an addition theorem for metalindelöf spaces which...
Following Malykhin, we say that a space is if contains a family of dense subsets such that and the intersection of every two elements of is nowhere dense, where is a nonempty open subset of is the of . We show that, for every cardinal , there is a compact extraresolvable space of size and dispersion character . In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) , 2) is extraresolvable and 3) is extraresolvable, where ...
It is shown that both the free topological group and the free Abelian topological group on a connected locally connected space are locally connected. For the Graev’s modification of the groups and , the corresponding result is more symmetric: the groups and are connected and locally connected if is. However, the free (Abelian) totally bounded group (resp., ) is not locally connected no matter how “good” a space is. The above results imply that every non-trivial continuous homomorphism...
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
Download Results (CSV)