On connected irresolvable Hausdorff spaces

Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...

Homogeneous Countable Connected Hausdorff Spaces

In 1925, P. Urysohn gave an example of a countable connected Hausdorff space [4]. Other examples have been contributed by R. Bing [l], M. Brown [2], and E. Hewitt [3]. Relatively few of the properties of such spaces have been examined. In this paper the question of homogeneity is studied. Theorem I shows that there exists a bihomogeneous countable connected Hausdorff space. Theorems II and III ...

Connected Mappings of Hausdorff Spaces

Strongly irresolvable spaces

Several new characterizations of strongly irresolvable topological spaces are found and precise relationships are noted between strong irresolvability, hereditary irresolvability, and submaximality. It is noted that strong irresolvablity is a faint topological property, while neither hereditary irresolvablity nor submaximality are semitopological.

On soft Hausdorff spaces

The aim of this paper is to study some properties of soft Hausdorff space introduced by Shabir and Naz. Firstly, we give a representation of soft sets and soft topological spaces. Secondly, we introduce some new concepts in soft topological space such as convergence of sequences, homeomorphism and investigate the relations between these concepts and Hausdorff axiom in soft topological space. 20...