{"title":"关于密实曲面的容量和深度","authors":"Mahboubeh Abbasi, Behrooz Mashayekhy","doi":"10.1007/s40062-020-00254-4","DOIUrl":null,"url":null,"abstract":"<p>K. Borsuk in 1979, at 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 <span>\\(g\\ge 0\\)</span> is equal to <span>\\(g+2\\)</span>. Also, we prove that the capacity and depth of a compact non-orientable surface of genus <span>\\(g>0\\)</span> is <span>\\([\\frac{g}{2}]+2\\)</span>.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"301 - 308"},"PeriodicalIF":0.5000,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00254-4","citationCount":"2","resultStr":"{\"title\":\"On the capacity and depth of compact surfaces\",\"authors\":\"Mahboubeh Abbasi, Behrooz Mashayekhy\",\"doi\":\"10.1007/s40062-020-00254-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>K. Borsuk in 1979, at 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 <span>\\\\(g\\\\ge 0\\\\)</span> is equal to <span>\\\\(g+2\\\\)</span>. Also, we prove that the capacity and depth of a compact non-orientable surface of genus <span>\\\\(g>0\\\\)</span> is <span>\\\\([\\\\frac{g}{2}]+2\\\\)</span>.</p>\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"15 2\",\"pages\":\"301 - 308\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-020-00254-4\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-020-00254-4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-020-00254-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
K. Borsuk in 1979, at 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 \(g\ge 0\) is equal to \(g+2\). Also, we prove that the capacity and depth of a compact non-orientable surface of genus \(g>0\) is \([\frac{g}{2}]+2\).
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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