The completion of the space of convex, bounded sets with respect to the Demyanov Metric

Andrzej Leśniewski , Tadeusz Rzeżuchowski , Jerzy Grzybowski

Abstract

The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.
Author Andrzej Leśniewski (FMIS / DODE)
Andrzej Leśniewski,,
- Department of Ordinary Differential Equations
, Tadeusz Rzeżuchowski (FMIS / DODE)
Tadeusz Rzeżuchowski,,
- Department of Ordinary Differential Equations
, Jerzy Grzybowski
Jerzy Grzybowski,,
-
Journal seriesDemonstratio Mathematica, ISSN 0420-1213
Issue year2013
Vol46
No1
Pages191-196
Publication size in sheets0.5
ASJC Classification2600 General Mathematics
URL http://demmath.mini.pw.edu.pl/archive/dm46_1/17.pdf
Languageen angielski
Score (nominal)11
ScoreMinisterial score = 8.0, 05-09-2019, ArticleFromJournal
Ministerial score (2013-2016) = 11.0, 05-09-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2013 = 0.58
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