Paracompact Topological Groups and Uniform Continuity
Partitioning bases of topological spaces
We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first-countable, 0-dimensional, Hausdorff space of size and weight which admits a point countable base without a partition to two bases.
P-embedding and product spaces
Point character of uniformities and completeness
Point-countable π-bases in first countable and similar spaces
It is a classical result of Shapirovsky that any compact space of countable tightness has a point-countable π-base. We look at general spaces with point-countable π-bases and prove, in particular, that, under the Continuum Hypothesis, any Lindelöf first countable space has a point-countable π-base. We also analyze when the function space has a point-countable π -base, giving a criterion for this in terms of the topology of X when l*(X) = ω. Dealing with point-countable π-bases makes it possible...
Powers of spaces of non-stationary ultrafilters
Prime mappings, number of factors and binary operations [Book]
Products and measurable cardinals
Products of convergence properties
Products of pseudoradial spaces.
Property and dominating families
Generalizations of earlier negative results on Property are proved and two questions on an -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ is regular” and “” the existence of a separable locally compact -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants...
Proximity classes of uniformities
Pseudouniform topologies on given by ideals
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.