Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topological semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces. Topological dynamics studies the asymptotic prope...

The concept of a topology for the fundamental group appears to have originated with Hurewicz (1935), but it has been actively studied only for the last ten years. The classical fundamental group of a pointed topological space X naturally inherits the quotient topology from the space of based loops in X endowed with the compact-open topology. The resulting space, called the topological fundament...

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every topological space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1 in that all its elements satisfy the topological inter...