On continuous extensions.
On -compactifications and -compactifiable spaces.
On Eberlein compactifications of metrizable spaces
We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.
On extension of the group operation over the Čech-Stone compactification
The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension...
On extensions of fuzzy topologies
On factorization of maps through τX
On finest unitary extensions of topological monoids
We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.
On functors of finite degree and -metrizable bicompact spaces.
On games of Topsoe.
On Hausdorff compactifications of non-locally compact spaces.
On Hausdorff Quotients of Spaces and Magill's Theorem.
On hereditary normality of , Kunen points and character
We show that is not normal, if is a limit point of some countable subset of , consisting of points of character . Moreover, such a point is a Kunen point and a super Kunen point.
On matrix points in Čech--Stone compactifications of discrete spaces
We prove the existence of -matrix points among uniform and regular points of Čech–Stone compactification of uncountable discrete spaces and discuss some properties of these points.
On non-normality points and metrizable crowded spaces
is non-normal for any metrizable crowded space and an arbitrary point .
On non-normality points, Tychonoff products and Suslin number
Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
On non-separable 0-dimensional metrizable spaces
On nowhere first-countable compact spaces with countable -weight
The minimum weight of a nowhere first-countable compact space of countable -weight is shown to be , the least cardinal for which the real line can be covered by many nowhere dense sets.
On one-point -compactification and local - compactness
On open maps and related functions over the Salbany compactification
Given a topological space , let and denote, respectively, the Salbany compactification of and the compactification map called the Salbany map of . For every continuous function , there is a continuous function , called the Salbany lift of , satisfying . If a continuous function has a stably compact codomain , then there is a Salbany extension of , not necessarily unique, such that . In this paper, we give a condition on a space such that its Salbany map is open. In particular,...
On paracompact uniform spaces