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The neutrality's origin, character, and extent are studied in the Neutrosophic set. The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applications. The neutrosophic set can find its spot to research because the universe is filled with indeterminacy. Neutrosophic set is currently being developed to express uncertain, imprecise, partial, and inconsistent data. Truth membership function, indeterminacymembership function, and falsitymembership function are used to express a neutrosophic set in order to address uncertainty. The neutrosophic set producesmore rational conclusions in a variety of practical problems. The neutrosophic set displays inconsistencies in data and can solve real-world problems. We are directed to do our work in semi-continuous and almost continuous mapping on the basis of the neutrosophic set by observing these. Since we are going to study the properties of semi continuous and almost continuous mapping, we present the meaning of N ~ semi-open set, N ~ semi-closed set, N ~ regularly open set, N ~ regularly closed set, N ~continuous mapping, N ~open mapping, N ~closed mapping, N ~semi-continuous mapping, N ~ semi-open mapping, N ~ semi-closed mapping. Additionally, we attempt to demonstrate a portion of their properties and furthermore referred to some examples. [ABSTRACT FROM AUTHOR]