On a generalization of uniformities
On dense subspaces satisfying stronger separation axioms
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
On minimal Hausdorff and minimal Urysohn functions
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
On minimal strongly KC-spaces
In this article we introduce the notion of strongly -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space is maximal countably compact if and only if it is minimal strongly , and apply this result to study some properties of minimal strongly -spaces, some of which are not possessed by minimal -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every...
On minimal--spaces
An -space is a topological space in which the topology is generated by the family of all -sets (see [N]). In this paper, minimal--spaces (where denotes several separation axioms) are investigated. Some new characterizations of -spaces are also obtained.
On -closed spaces.
On projectiveness in H-closed spaces
On R-compact spaces
On strongly connected spaces
On --open sets and a decomposition of almost--continuity.
On --open sets.