On continuous extensions.
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.
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...
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.
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.
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.
is non-normal for any metrizable crowded space and an arbitrary point .
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.
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.
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,...