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.
MALEKI, HASSAN and MOLAEI, MOHAMMADREZA
Turkish Journal of Mathematics: Vol. 39:
6, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss6/6