Generalized open sets in grill N-topology

Abstract

The aim of this paper is to give a systematic development of grill Ntopological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N -topological spaces and discuss the relationships between them.2010 MSC: 54A05; 54A99; 54C10.

An Innovative Approach of N-Soft Quotient Topological Space

“…Recently, in 2016, ivagar et al [4] introduced and established the theory of N-topological space from the geometric existence of topological space. Also, they derived various forms of quotient topology from quotient mappings [5]; in particular, they defined α-quotient mappings, strongly α-quotient mappings, and α * -quotient mappings between topological spaces.…”

Theory of g-T_g-Maps

“…As in the papers of [5,10,15,29,30], among others, the manner we have positioned the arrows is solely to stress that, in general, none of the implications in Figs 1, 2 and 1 is reversible.…”

“…The concepts 1 of (T Ω , T Σ )-map π : T Ω → T Σ [1,2], g-(T Ω , T Σ )-map π g : T Ω → T Σ [9,18], (T g,Ω , T g,Σ )-map π : T g,Ω → T g,Σ [3], and g-(T g,Ω , T g,Σ )-map π g : T g,Ω → T g,Σ [21], called, respectively, ordinary and generalized maps (briefly, T-map and g-T-map, respectively) between T -spaces T Ω and T Σ , and ordinary and generalized maps (briefly, T g -map and g-T g -map, respectively) between T g -spaces T g,Ω and T g,Σ are all fundamental concepts that have been introduced and investigated by several mathematicians [12,16,17,20,21,23,29,31,33].…”

On Grill Sβ-Open Set in Grill Topological Spaces

“…The idea of disintegration of Cty on a GTS and some families of sets were characterized to Grl in [26][27][28].…”

“…The notion of soft Grl, soft operators, precontinuity and soft topology τ G were defined and discussed by Saif and Al-Muntaser [25]. The idea of disintegration of Cty on a GTS and some families of sets was characterized to Grl in [26][27][28]. Thorn [29] proved that Grls are always a union of ultra-filters.…”