On the Capacity and Depth of Compact Surfaces

Mahboubeh Abbasi; Behrooz Mashayekhy

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arXiv · 1612.03335

On the Capacity and Depth of Compact Surfaces

Mahboubeh Abbasi·Behrooz Mashayekhy

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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 $g\geq 0$ is equal to $g+2$. Also, we prove that the capacity and depth of a compact non-orientable surface of genus $g>0$ is $[\frac{g}{2}]+2$.

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Mahboubeh Abbasi, Behrooz Mashayekhy. 2016-12-10. On the Capacity and Depth of Compact Surfaces. https://arxiv.org/abs/1612.03335

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