Finite relational structure models of topological spaces and maps

Finite Topological Spaces

(1) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i < len f holds πi f πi+1 f : Let i, j be natural numbers. If i j and 1 i and j len f ; then πi f π j f : (2) Let A be a set and f be a finite sequence of elements of 2A. Suppose that for every natural number i such that 1 i and i< len f holds πi f πi+1 f : Let i, j be natu...

Finite Topological Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Poset models of topological spaces

We consider poset models of topological spaces and show that every T1-space has an bounded complete algebraic poset model, thus give a positive answer to a question asked in a recent paper by Waszkiewicz. It is also proved that every T1-space is homeomorphic to the maximal point space of a d-space. In the classic general topology, people are mainly interested in the spaces which satisfy at leas...

The Euler Characteristic of Finite Topological Spaces

The purpose of this paper is to illustrate the relationship between the topological property of the Euler characteristic and a combinatorial object, the Möbius function, in the context of finite T0-spaces. To do this I first explain the fundamental connection between such spaces and finite partially ordered sets by proving some facts fundamental to the study of finite spaces. Then I define the ...