-generalized closed sets.
Magill-type theorems for mappings.
Mapping theorems on countable tightness and a question of F. Siwiec
In this paper -quotient maps and -spaces are introduced. It is shown that (1) countable tightness is characterized by -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) -spaces are characterized as the -quotient images of metric spaces; (4) assuming , a compact -space is an -space if and only if every countably compact subset...
Mappings and decompositions of continuity on almost Lindelöf spaces.
Mappings and inductive invariants
Mappings on -paracompact spaces.
Martin’s Axiom and -resolvability of Baire spaces
We prove that, assuming MA, every crowded space is -resolvable if it satisfies one of the following properties: (1) it contains a -network of cardinality constituted by infinite sets, (2) , (3) is a Baire space and and (4) is a Baire space and has a network with cardinality and such that the collection of the finite elements in it constitutes a -locally finite family. Furthermore, we prove that the existence of a Baire irresolvable space is equivalent to the existence of...
Maximal ideals in the Lie algebra of vector fields
Maximal nowhere dense -sets in basically disconnected spaces and -spaces
In [5] the following question was put: are there any maximal n.d. sets in ? Already in [9] the negative answer (under MA) to this question was obtained. Moreover, in [9] it was shown that no -set can be maximal n.d. In the present paper the notion of a maximal n.d. -set is introduced and it is proved that under CH there is no such a set in . The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. -sets...
Maximal pseudocompact spaces and the Preiss-Simon property
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...
Maximal p-Systems and Realcompleteness.
Mazur spaces.
Means on scattered compacta
We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.
Measure and measurable functions of
Measure theoretic behavior of closed sets
Measures of Lindelöf and separability in approach spaces.
Measures on Corson compact spaces
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
Measure-Theoretic Characterizations of Certain Topological Properties
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.
Measure-theoretic characterizations of hereditarily-normal spaces.
Menger's Theorem for topological spaces