θ s -open sets and θ s -continuity of maps in the product space

Abstract

In this study, the concept of θ s -open set is introduced. The topology formed by θ s -open sets is strictly finer than the topology formed by θ-open sets but is not comparable with the topology formed by ω θ -open sets. Related concepts such as θ sopen and θ s -closed functions, θ s -continuous function, θ s -connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of θ s -continuous function from an arbitrary topological space into the product space is investigated further.

حول الدوال المستمره الضعيفه من النمط Θ و Δ

“…Many authors defined and introduced a generalization form of open sets and weak and strong forms of semi-open sets see in [2][3][4][5][6] . The concept FC functions have the attention of many authors see for example 7 . First, a point ӽӼ is called an 𝜃 -Cluster point of E⊆ Ӽ if E non-trivially intersects the closure of each open set containing ӽ in Ӽ.…”

Topological-like notions via Δ-open sets

“…Recently, the idea of introducing new classes of open-like and closed-like sets in topological spaces is still attracting many researchers, for example [1][2][3][4][5], [8], [11], [14], [16], [20], [21], and [22].…”