Topological nearly entropy

Topological Nearly Entropy on Nearly Compact Spaces

“…Moreover this paper presenting the notion of topological nearly entropy for Rmap on nearly compact space and some its fundamental properties are studied. These fundamental properties are further extension of Gulamsarwar and Salleh [9] topological nearly entropy. Furthermore, we introduce R-space in order to study the effect of nearly compactness on Hausdorff space to the topological nearly entropy.…”

“…A function f : X → Y is called R-map [5] if the inverse image of every regular open set in Y is regular open in X. If f : X → X is an R-map, then the pair (X, f ) is called topological R-dynamical system, and if X is nearly compact, (X, f ) is called nearly compact R-dynamical system, see [9]. Now, we recall some definitions of topological nearly entropy and its fundamental properties from [9] as follows.…”

“…Definition 2.1. [9] Let (X, f ) be a topological R-dynamical system, U be a regular open cover of X and K be a nonempty nearly compact relative to the space X such…”

“…In a recent paper, Gulamsarwar and Salleh [9] presented a new generalized notion of topological entropy on nearly compact space by using R-map [5], namely topological nearly entropy. Recall that every compact space is nearly compact but not the converse.…”

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In our previous paper [9], we have introduced topological nearly entropy, Ent N (f ) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied.

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