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<p>This paper is based on the problems of diversifying the topological complexity number in discrete spaces (simplicial complexes) and establishing a relationship between the parametrized version of the TC and the targeted version of the TC in usual topological spaces. Specifically, certain topological complexity numbers, such as both the relative and the discrete version of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2908_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {TC}_{{n}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>TC</mtext> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>, and both the discrete and the parametrized version of the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2908_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {TC}_{{n}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>TC</mtext> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>, are introduced on the simplicial version.</p>

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Some Notes and Comparisons on Topological Complexities

  • 期刊论文

  • 发表日期：

    2025年7月20日

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  • Melih İs

摘要

This paper is based on the problems of diversifying the topological complexity number in discrete spaces (simplicial complexes) and establishing a relationship between the parametrized version of the TC and the targeted version of the TC in usual topological spaces. Specifically, certain topological complexity numbers, such as both the relative and the discrete version of the \(\hbox {TC}_{{n}}\) TC n , and both the discrete and the parametrized version of the \(\hbox {TC}_{{n}}\) TC n , are introduced on the simplicial version.