Top spaces

Local Lie groups and local top spaces

“…If p : I Â K ! G is a mapping, then K Â G Â I with the product ðk; g; iÞðk 1 ; g 1 ; i 1 Þ ¼ ðk; gpði; k 1 Þg 1 ; i 1 Þ is a generalized group, which is called Rees matrix semigroup denoted by MðG; I; K; pÞ [2]. Theorem 1.1 [2].…”

“…T ; m 2 ðx; yÞ ¼ xy are continuous maps. Definition 1.2 [2]. A topological generalized group ðT; ÁÞ is called a top space if:…”

T-Spaces

“…Thus, T x is a closed subset of T and then we can say it is a closed generalized subgroup of T . Now for continuing we need the definition of top spaces that are introduced in [18]. The topological generalized group T is said to be a top space if T is a manifold and the generalized group operations m 1 and m 2 are smooth [18].…”

“…The role of identity as a mapping lead to many new important challenges. Generalized groups have been applied in genetic [1,16], geometric [15], and dynamical systems [17]. The notion of generalized action [12] is an extension of the notion of group actions [4,7].…”

“…Now for continuing we need the definition of top spaces that are introduced in [18]. The topological generalized group T is said to be a top space if T is a manifold and the generalized group operations m 1 and m 2 are smooth [18]. As shown in [6], if X is a manifold and Card (e(T )) < ∞ , then we can show that for x ∈ X , T x is a generalized subtop space of T and also a topological generalized subgroup of T .…”