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Title

LS-CATEGORY AND TOPOLOGICAL COMPLEXITY

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Abstract

 LUSTERNIK-SCHNIRELMANN CATEGORY (OR SIMPLY LS-CAT) IS A MEASURE OF COMPLEXITY OF TOPOLOGICAL SPACE. IT IS A TOPOLOGICAL INVARIANT DEFINED TO BE THE LEAST INTEGER N SUCH THAT THERE EXISTS AN OPEN COVERING SET OF N + 1 OPEN SETS WITH EACH OPEN SET CONTRACTIBLE TO A POINT IN THE WHOLE SPACE. ON THE OTHER HAND TOPOLOGICAL COMPLEXITY (OR SIMPLY TC) OF A SPACE IS AN INTEGER INVARIANT MEASURING THE COMPLEXITY OF THE PROBLEM OF NAVIGATION IN A TOPOLOGICAL SPACE WHICH DEPENDS ONLY ON THE HOMOTOPY TYPE OF TOPOLOGICAL SPACE. WE CONSIDER THE RELATION BETWEEN LS-CAT AND TC OF SOME SPECIFIC TOPOLOGICAL SPACES.

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    • Cite

    APA: Copy

    Bayeh, Marzieh. (2012). LS-CATEGORY AND TOPOLOGICAL COMPLEXITY. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/925998/en

    Vancouver: Copy

    Bayeh Marzieh. LS-CATEGORY AND TOPOLOGICAL COMPLEXITY. 2012. Available from: https://sid.ir/paper/925998/en

    IEEE: Copy

    Marzieh Bayeh, “LS-CATEGORY AND TOPOLOGICAL COMPLEXITY,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2012, [Online]. Available: https://sid.ir/paper/925998/en

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