On the Capacity and Depth of Compact Surfaces

2016/12/10 by Mahboubeh Abbasi, Abbasi, Mahboubeh, Behrooz Mashayekhy +1 · 1 citation
Mathematics · #55P15 #55P20 #55P55 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P15 #msc:55P20 #msc:55P55

paper · pdf · doi:10.48550/arxiv.1612.03335

9 pages, recommended to Journal of Homotopy and Related Structures

arxiv created 2019/10/29 · arxiv updated 2019/10/31

Abstract

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of capacity and depth of a compactum. In this paper, we compute the capacity and depth of compact surfaces. We show that the capacity and depth of every compact orientable surface of genus g≥ 0 is equal to g+2. Also, we prove that the capacity and depth of a compact non-orientable surface of genus g>0 is [(g)/(2)]+2.

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