A natural Galois connection between generalized norms and metrics
Having in mind a well-known connection between norms and metrics on vector spaces, for an additively written group X, we establish a natural Galois connection between functions of X to ℝ and X2 to ℝ.
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| Format: | Article |
| Language: | English |
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Sciendo
2017-12-01
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| Series: | Acta Universitatis Sapientiae: Mathematica |
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| Online Access: | https://doi.org/10.1515/ausm-2017-0027 |
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doaj-e92076804bd24a56a2e70feba42c81622021-09-06T19:40:20ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522017-12-019236037310.1515/ausm-2017-0027ausm-2017-0027A natural Galois connection between generalized norms and metricsSzáz Árpád0Department of Mathematics, University of Debrecen, H–4002Debrecen, Pf. 400, HungaryHaving in mind a well-known connection between norms and metrics on vector spaces, for an additively written group X, we establish a natural Galois connection between functions of X to ℝ and X2 to ℝ.https://doi.org/10.1515/ausm-2017-0027groupspreseminormsinvariant semimetricsgalois connectionso6a1520a9954e25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Száz Árpád |
| spellingShingle |
Száz Árpád A natural Galois connection between generalized norms and metrics Acta Universitatis Sapientiae: Mathematica groups preseminorms invariant semimetrics galois connections o6a15 20a99 54e25 |
| author_facet |
Száz Árpád |
| author_sort |
Száz Árpád |
| title |
A natural Galois connection between generalized norms and metrics |
| title_short |
A natural Galois connection between generalized norms and metrics |
| title_full |
A natural Galois connection between generalized norms and metrics |
| title_fullStr |
A natural Galois connection between generalized norms and metrics |
| title_full_unstemmed |
A natural Galois connection between generalized norms and metrics |
| title_sort |
natural galois connection between generalized norms and metrics |
| publisher |
Sciendo |
| series |
Acta Universitatis Sapientiae: Mathematica |
| issn |
2066-7752 |
| publishDate |
2017-12-01 |
| description |
Having in mind a well-known connection between norms and metrics on vector spaces, for an additively written group X, we establish a natural Galois connection between functions of X to ℝ and X2 to ℝ. |
| topic |
groups preseminorms invariant semimetrics galois connections o6a15 20a99 54e25 |
| url |
https://doi.org/10.1515/ausm-2017-0027 |
| work_keys_str_mv |
AT szazarpad anaturalgaloisconnectionbetweengeneralizednormsandmetrics AT szazarpad naturalgaloisconnectionbetweengeneralizednormsandmetrics |
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1717768739878862848 |