In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic pT1 2 space and neutrosophic gpT1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples. Keywords: neutrosophic topology; neutrosophic generalized topology; neutrosophic generalized pre-closed sets; neutrosophic generalized pre-open sets; neutrosophic pT1 2 space; neutrosophic gpT1 2 space; generalized neutrosophic compact and generalized neutrosophic compact

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In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper

In this paper, we introduce the notations of e-I-open sets and strong B * I -set to obtain a decomposition of continuing via idealization. Additionally, we investigate properties of e-I-open sets and strong B * Iset. Also we studied some more properties of e-I-open sets and obtained several characterizations of e-I-continuous functions and investigate their relationship with other types of functions.

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