Additive involutions and Hamel bases
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| 024 | 7 | 0 | |a 10.1007/s00010-013-0241-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-013-0241-7 | ||
| 100 | 1 | |a Jabłoński |D Wojciech |u Department of Mathematics, University of Rzeszow, Rejtana 16 A, 35-310, Rzeszów, Poland |4 aut | |
| 245 | 1 | 0 | |a Additive involutions and Hamel bases |h [Elektronische Daten] |c [Wojciech Jabłoński] |
| 520 | 3 | |a Our aim is to give other proofs of some slight generalizations of results from Baron (Aequat Math, 2013). We describe larger classes of discontinuous additive involutions $${a:X\to X}$$ a : X → X on a topological vector space X such that $${a(H)\setminus H\neq\emptyset}$$ a ( H ) \ H ≠ ∅ holds for a sufficiently numerous set $${H\subset X}$$ H ⊂ X of vectors linearly independent over $${{\mathbb{Q}}}$$ Q . We also consider the topological vector space $${{\mathcal{A}}_X}$$ A X of all additive functions $${a:X\to X}$$ a : X → X with the topology induced by the Tychonoff topology of the space X X . We prove in a simple way that some classes of discontinuous additive involutions are dense in the topological vector space $${{\mathcal{A}}_X}$$ A X . | |
| 540 | |a The Author(s), 2013 | ||
| 690 | 7 | |a Additive function |2 nationallicence | |
| 690 | 7 | |a involution |2 nationallicence | |
| 690 | 7 | |a Hamel base |2 nationallicence | |
| 690 | 7 | |a Tychonoff topology |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 575-582 |x 0001-9054 |q 89:3<575 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-013-0241-7 |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/s00010-013-0241-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Jabłoński |D Wojciech |u Department of Mathematics, University of Rzeszow, Rejtana 16 A, 35-310, Rzeszów, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 575-582 |x 0001-9054 |q 89:3<575 |1 2015 |2 89 |o 10 | ||