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In the current paper, particular acheivments of single-valued neutrosophic continuity on a singlevalued neutrosophic topological space (𝔗 ̃, 𝜏̃𝛾̃, 𝜏̃𝜂̃, 𝜏̃𝜇̃) are introduced. Some necessary implications between them are illustrated. The theories of r-single-valued neutrosophic compact, r-single-valued neutrosophic ideal compact, r-single-valued neutrosophic quasi H-closed and r-single-valued neutrosophic compact modulo an single-valued neutrosophic ideal I~ are presented and investigated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce various types of r-single-valued neutrosophic open sets based on the single-valued neutrosophic ideals in Decomposition of Š ostak Sense. Different mappings of single-valued continuity and ideal continuity based on the r-single-valued neutrosophic ideal openness are defined and many implications between them are investigated with counterexamples illustrated. [ABSTRACT FROM AUTHOR]