Two new minimality concepts are defined and investigated in fuzzy spaces. Relationships between them and the known one are obtained. Several results concerning them are obtained. The results especially deal with products, separation axioms, maps, and fuzzy topologically generated topologies.

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms T0 and T1. Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

The density topologies with respect to measure and category are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied.

In this note, we introduce the degree to which an I-fuzzy topological space (X, τ) is Sub T 1 (in short, ST 1), which we denote by ST 1 (X, τ) and proved that KT 1 (X, τ), defined by Yue and Fang and ST 1 (X, τ) are equal.

In this paper, the concepts of soft generalized μ-T0, soft generalized μ-T1, soft generalized Hausdorff, soft generalized regular, soft generalized normal and soft generalized completely regular spaces in Soft Generalized Topological Spaces are defined and studied. Further some of its properties and characterizations are established.

Abstract The aim of this paper is to introduce some new separation axioms based on the idea defining kinds open sets, namely semi- θ -open sets. We study there basic properties and also implications these among themselves with known T 2 ,T 1 0 are obtained.