In this paper, we introduce and investigate several new concepts in the framework of single-valued neutrosophic soft ideal topological spaces, including $ \mathbf{t} $-single valued neutrosophic soft $ \delta\mathcal{I} $-cluster points and $ \theta\mathcal{I} $-cluster points, together with their corresponding $ \delta \mathcal{I} $-closure and $ \theta\mathcal{I} $-closure operators. We further study $ \mathbf{t} $-single valued neutrosophic soft $ \delta\mathcal{I} $-closed and $ \theta\mathcal{I} $-closed sets and examine their fundamental properties. In addition, various types of continuity are introduced and analyzed, such as single-valued neutrosophic soft $ \delta \mathcal{I} $-continuity, $ \theta\mathcal{I} $-continuity, and almost $ \mathcal{I} $-continuity, along with stronger forms including strongly $ \theta $-ideal continuity and almost ideal continuity. Moreover, the notions of single-valued neutrosophic soft $ \mathcal{I} $-regular and almost $ \mathcal{I} $-regular spaces are established within this setting, and several relationships among these concepts are derived, providing a deeper understanding of their structural properties and potential applications.
Citation: Yaser Saber. On some topological properties in single-valued neutrosophic soft ideal spaces[J]. AIMS Mathematics, 2026, 11(8): 26136-26167. doi: 10.3934/math.20261047
In this paper, we introduce and investigate several new concepts in the framework of single-valued neutrosophic soft ideal topological spaces, including $ \mathbf{t} $-single valued neutrosophic soft $ \delta\mathcal{I} $-cluster points and $ \theta\mathcal{I} $-cluster points, together with their corresponding $ \delta \mathcal{I} $-closure and $ \theta\mathcal{I} $-closure operators. We further study $ \mathbf{t} $-single valued neutrosophic soft $ \delta\mathcal{I} $-closed and $ \theta\mathcal{I} $-closed sets and examine their fundamental properties. In addition, various types of continuity are introduced and analyzed, such as single-valued neutrosophic soft $ \delta \mathcal{I} $-continuity, $ \theta\mathcal{I} $-continuity, and almost $ \mathcal{I} $-continuity, along with stronger forms including strongly $ \theta $-ideal continuity and almost ideal continuity. Moreover, the notions of single-valued neutrosophic soft $ \mathcal{I} $-regular and almost $ \mathcal{I} $-regular spaces are established within this setting, and several relationships among these concepts are derived, providing a deeper understanding of their structural properties and potential applications.
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Yaser Saber. On some topological properties in single-valued neutrosophic soft ideal spaces[J]. AIMS Mathematics, 2026, 11(8): 26136-26167. doi: 10.3934/math.20261047
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