Semi-Global Aspects of Uryshon’s Lemma and Broken Two Sheets Spaces

Prohelika Das

Abstract

In this paper we give a semi-global description of what is known as the well known Uryshon’s Lemma in classical topology. Giving up the usual notions of open and closeness in a topological space (X, TX) where TX is a topology, we deal with a pair (X, SX) with an arbitrary subset SX of power set P(X) of X . Thus we deal with a semi-global character where so-called open or closed character in such spaces treated in reference to some specific pseudo continuous types of maps. Keeping this in note, we explore some characteristics with so-called topological flavour in such a space (X, SX), which may be considered as some sort of analytical description of available classical topological notion.