Weak Insertion of a γ − Continuous Function1

Insertion of a gamma-continuous function

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

insertion of a gamma-continuous function

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Udc 517.98 Weak Insertion of a Continuous Function between Two Comparable Functions1

The concept of a pre-open set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called pre-open or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called pre-closed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, pre-open, was used for the first time by A. S. Mashhour, M. E. Abd El-M...

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

On weak Γ-(semi)hypergroups