Minimal spaces with a mathematical structure

Abstract

This paper will discuss, grill topological space which is not only a space for obtaining a new topology but generalized grill space also gives a new topology. This has been discussed with the help of two operators in minimal spaces.

New Operators in Ideal Topological Spaces and Their Closure Spaces

“…Hayashi [6], Hashimoto [7], Newcomb [8], Modak [9,10], Bandyopadhyay and Modak [11,12], Noiri and Modak [13], Al-Omari et al [14,15,16,17] have enriched this study. Natkaniec in [18] have introduced the complement of local function and it is called  -Operator.…”

Set operators and associated functions

“…(vi) For a grill minimal space (X; M; G 1 ), the operator () M is associated with the operator M [13].…”

Common properties and approximations of local function and set operator $\psi$

“…[18] called such ideal as ' -boundary' whereas Dontchev [27] called such spaces as 'Hayashi-Samuel' spaces. In fact such ideals play a very important role in the study of ideals (see: [6,19,28,29,30]).…”

“…The study of ideals on topological spaces was first introduced by K. Kuratowski [1]. The authors, Al-Omari and Noiri [2,3], Modak [4,5,6], Modak and Islam [7,8,9,10], Ekici and Elmali [11], Modak and Mistry [12], Khan and Noiri [13], Csaszar [14], O zbakir and Yildirim [15] have introduced the study of ideals on the generalized topological space. We know from [1] that, a subcollection of () X  , the powerset of X , is called an ideal on X if (i) for , A B X  and AB , A (hereditary) and (ii) for , A B X  and , AB , AB  (finite additivity).…”