Sequentially Hausdorff and full sequentially Hausdorff spaces

Historic set carries full hausdorff dimension

‎We prove that the historic set for ratio‎ ‎of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional‎ ‎non-uniformly hyperbolic dynamical systems.

Modal compact Hausdorff spaces

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

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...

Extensions of 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...