A local stability principle for continuous group homomorphisms in nonstandard setting
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| 003 | CHVBK | ||
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| 008 | 210128e20150801xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0301-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0301-7 | ||
| 245 | 0 | 2 | |a A local stability principle for continuous group homomorphisms in nonstandard setting |h [Elektronische Daten] |c [Filip Sládek, Pavol Zlatoš] |
| 520 | 3 | |a We state a simple fact relating some continuity and homomorphy properties of an internal mapping between nonstandard extensions of topological groups and the nonstandard extension of the "observable trace” of the map, which can be interpreted as a kind of stability principle. This leads to a strengthening of two formerly proved (standard) stability results (a global one and a local one) along with simplifying their proofs. We show that every "sufficiently continuous,” "reasonably bounded” and "sufficiently homomorphic” mapping from a locally compact to an arbitrary topological group is "arbitrarily close” to a continuous homomorphism between them. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Nonstandard analysis |2 nationallicence | |
| 690 | 7 | |a topological group |2 nationallicence | |
| 690 | 7 | |a continuous homomorphism |2 nationallicence | |
| 690 | 7 | |a stability |2 nationallicence | |
| 700 | 1 | |a Sládek |D Filip |u Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia |4 aut | |
| 700 | 1 | |a Zlatoš |D Pavol |u Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 991-1001 |x 0001-9054 |q 89:4<991 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0301-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0301-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Sládek |D Filip |u Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zlatoš |D Pavol |u Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 991-1001 |x 0001-9054 |q 89:4<991 |1 2015 |2 89 |o 10 | ||