Generalized Topological Groups and Genetic Recombination

Abstract

In this paper we introduce topological and algebraic structures on the space of DNA sequences. The idea of these structures comes from genetic recombination.

Topological Characterizations for Sheaf of the Groups Formed by Topological Generalized Groups

“…Furthermore this kind of structure appears in genetic codes. Generalized groups have been applied to DNA analysis by transforming the set of DNA sequences to generalized group in [1].…”

T-Spaces

“…Moreover, the mapping e : T → T defined by t → e(t) is a continuous map. Note that in a topological generalized group, property (1) implies that…”

“…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].…”

“…Definition 2.1 [1,14] A topological generalized group is a Hausdorff topological space T that is endowed with a generalized group structure such that the generalized group operations m 1 : T → T defined by t → t −1 and…”

Generalized crossed modules and group-groupoids

“…With this property, every group is a generalized group. After Molaei gave the definition of a generalized group, this concept was studied in terms of algebraic, topological, and differentiable in large various areas of mathematics [1,2,8,[12][13][14][15].…”