Spaces of Locally Convex Curves in S and Combinatorics of the Group B

Topological number for locally convex topological spaces with continuous semi-norms

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

Classification of spaces of locally convex curves in S n and combinatorics of the Weyl group D n + 1 Nicolau C . Saldanha and Boris Shapiro March 22 , 2007

In 1920’s Marston Morse developed what is now known as Morse theory trying to study the topology of the space of closed curves on S2, see [7] and [5]. 80 years later a very similar problem about the topology of the space of closed and locally convex (i.e. without inflection points) curves on S2 is still widely open. The main difficulty is the absence of the covering homotopy principle for the m...

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

SOME FIXED POINT THEOREMS IN LOCALLY CONVEX TOPOLOGY GENERATED BY FUZZY N-NORMED SPACES

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

Classification of spaces of locally convex curves in S n and combinatorics of the Weyl group D n + 1 Nicolau C . Saldanha and Boris Shapiro