In this paper, minimal γ-semi-open sets in topological spaces introduce and discuss. Also some properties of pre γ-semi-open sets using properties of minimal γ-semi-open sets obtain. As an application of a theory of minimal γ-semi-open sets, I obtain a sufficient condition for a γ-semi-locally finite space to be a pre γ-semi-T2 space.

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

In this paper we introduce and study the neutrosophic crisp pre-open, semi-open, βopen set, neutrosophic crisp continuity and neutrosophic crisp compact spaces are introduced. Furthermore, we investigate some of their properties and characterizations. Possible application to GIS topology rules are touched upon.

The aim of this paper is to investigate some properties of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces. Some relationships of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces are discussed. Moreover, decompositions of continuity are provided. 2000 Mathematics Subject Classification: 54A05, 54A10, 54C08, 54C10.

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy α-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. In this paper the concepts of fuzzy α-quotient maps, fuzzy semi quotien...

Open set classification (OSC) tackles the problem of determining whether data are in-class or out-of-class during inference, when only provided with a examples at training time. Traditional OSC methods usually train discriminative generative models owned data, and then utilize pre-trained to classify test directly. However, these always suffer from embedding confusion problem, i.e., partial ins...