Generalized $${G_\delta}$$ G δ -submaximal spaces

Generalized Topologies on Finite Sets

“…Let X = {a, b, c}. Then by the above proposition GT (3, 7) = 3, GT (3, 6) = 9, GT (3, 5) = 13, GT (3, 4) = 15, GT (3, 3) = 12 and GT (3, 2) = 7 GT (3, 1) = 1 = GT (3,8). Thus, the total number of generalized topologies on X is …”

“…A GT on X is a joinsublattice (expX, ⊆) with the minimum element ∅, denoted by 0. Some important counterexamples in topological spaces or GTS can be found in the finite forms (see for example, [1,3]). …”

Some Properties of Generalized Topologies in GTSs

“…A GTS (X, µ) is called µ-extremally disconnected or simply, extremally-disconnected [4] A generalized topological space (X, µ) is said to be a generalized G δ -submaximal space [1] if every µ-dense subset of X is a µ-G δ -set in X.…”

“…Let (X, µ) be a generalized topological space. Then x ∈ X is called µ-isolated [1] if {x} is µ-open. If every point of X is µ-isolated, then X is called µ-discrete [1].…”

Submaximality on Bigeneralized Topological Spaces

“…Based on this, some mathematicians established some new results for generalized submaximal space e.g. [9,19]. In 2016, Ahmadi Zand et.al gave few results for submaximal space and defined a space namely, generalized G δ -submaximal space, and studied the nature of this space [19].…”