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The Small Inductive Dimension of Subsets of Alexandroff Spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Chonbuk National University, South Korea.
Shimane University, Japan.
2016 (English)In: Filomat, ISSN 0354-5180, Vol. 30, no 11, 3007-3014 p.Article in journal (Refereed) Published
Abstract [en]

We describe the small inductive dimension ind in the class of Alexandroff spaces by the use of some standard spaces. Then for ind we suggest decomposition, sum and product theorems in the class. The sum and product theorems there we prove even for the small transfinite inductive dimension trind. As an application of that, for each positive integers k, n such that k amp;lt;= n we get a simple description in terms of even and odd numbers of the family S(k, n) = {S subset of K-n : vertical bar S vertical bar = k + 1 and ind S = k}, where K is the Khalimsky line.

Place, publisher, year, edition, pages
UNIV NIS, FAC SCI MATH , 2016. Vol. 30, no 11, 3007-3014 p.
Keyword [en]
small inductive dimension; Khalimsky line; Alexandroff space
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-135003DOI: 10.2298/FIL1611007CISI: 000393212700012OAI: oai:DiVA.org:liu-135003DiVA: diva2:1078719
Note

Funding Agencies|National Research Foundation of Korea(NRF) - Ministry of Education, Science and Technology [2016R1D1A3A03918403]; Japan Society for the Promotion of Science [22540084]

Available from: 2017-03-06 Created: 2017-03-06 Last updated: 2017-11-29

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CiteExportLink to record
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  • Other style
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  • de-DE
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  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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