| Summary: | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <msub> <mi>T</mi> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msub> </mrow> </semantics> </math> </inline-formula> space and neutrosophic <inline-formula> <math display="inline"> <semantics> <mrow> <mi>g</mi> <mi>p</mi> <msub> <mi>T</mi> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msub> </mrow> </semantics> </math> </inline-formula> 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.
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