| Summary: | This paper aims to mark out new terms of single-valued neutrosophic notions in a Šostak sense called single-valued neutrosophic semi-closure spaces. To achieve this, notions such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>-closure operators and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>-interior operators are first defined. More precisely, these proposed contributions involve different terms of single-valued neutrosophic continuous mappings called single-valued neutrosophic (almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>, faintly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>, weakly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mi>£</mi></mrow></semantics></math></inline-formula>-continuous. Finally, for the purpose of symmetry, we define the single-valued neutrosophic upper, single-valued neutrosophic lower and single-valued neutrosophic boundary sets of a rough single-valued neutrosophic set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi>n</mi></msub></semantics></math></inline-formula> in a single-valued neutrosophic approximation space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mover accent="true"><mi mathvariant="script">F</mi><mo>˜</mo></mover><mo>,</mo><mi>δ</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. Based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mi>n</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>, we also introduce the single-valued neutrosophic approximation interior operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>int</mi><msub><mi>α</mi><mi>n</mi></msub><mi>δ</mi></msubsup></semantics></math></inline-formula> and the single-valued neutrosophic approximation closure operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>Cl</mi><msub><mi>α</mi><mi>n</mi></msub><mi>δ</mi></msubsup></semantics></math></inline-formula>.
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