Characterization of ultra separation axioms via -kernel.
Closed copies of the rationals
Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property
In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property . It follows that it is consistent that closed discrete subsets of a separable space which are also relatively normal (relatively countably paracompact, relatively ) in are necessarily countable. There are, however, consistent examples of...
Closed subsets of absolutely star-Lindelöf spaces II
In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed subspace.
Closure, interior, and union in finite topological spaces
Continuous images of Lindelöf -groups, -compact groups, and related results
It is shown that there exists a -compact topological group which cannot be represented as a continuous image of a Lindelöf -group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf -groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space is a continuous image of a Lindelöf -group, then there exists a covering of by dyadic compacta such that . We also show that if a homogeneous compact space is a continuous...
Countable compactness of lexicographic products of GO-spaces
We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see: