T-Spaces

Authors : Hassan Maleki, Mohammadreza Molaei

Pages : 851-863

View : 11 | Download : 9

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper, using generalized groups and their generalized actions, we define and study the notion of $T$-spaces. We study properties of the quotient space of a $T$-space and we present the conditions that imply the Hausdorff property for it. We also prove some essential results about topological generalized groups. As a main result, we show that for each positive integer $n$ there is a topological generalized group $T$ with $n$ identity elements. Moreover, we study the maps between two $T$-spaces and we consider the notion of $T$-transitivity.
Keywords : Generalized group, generalized action, transitivity, $T$-space, quotient space