On minimal Hausdorff spaces

Minimal sequential Hausdorff spaces

A sequential space (X,T) is called minimal sequential if no sequential topology on X is strictly weaker than T . This paper begins the study of minimal sequential Hausdorff spaces. Characterizations ofminimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of s...

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...

Topology Proceedings 9 (1984) pp. 243-268: BETWEEN MINIMAL HAUSDORFF AND COMPACT HAUSDORFF SPACES

Hausdorff measure on o-minimal structures

In [Berarducci-Otero, 2004], the authors define an analogue of Lebesgue measure for bounded definable subsets of an o-minimal structure K , which expands a real closed field. Our aim is defining the area of a bounded definable d-dimensional subsets of Kn. Different possible definitions for such area are possible: we will prove that some of them are equivalent. On the reals, there are many diffe...

Function spaces and Hausdorff dimension on fractals

We start by surveying a possible approach for function spaces of Besov type on special closed subsets of Rn. Afterwards we recall that, in the case of Sobolev spaces and Besov spaces on Rn, the Hausdorff dimension for the graphs of continuous functions belonging to such spaces has been studied by several authors, and that in the case of Besov spaces the final answer concerning the maximal possi...