On orthogonally additive injections and surjections

• Autorzy: Karol Baron
• Języki publikacji: EN

Abstrakty

EN

Let \(E\) be a real inner product space of dimension at least 2 and \(V\) a linear topological Hausdorff space. If \(\operatorname{card}E\leq \operatorname{card} V\), then the set of all orthogonally additive injections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology. If \(\operatorname{card}V\leq \operatorname{card}E\), then the set of all orthogonally additive surjections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology.

Słowa kluczowe

EN

orthogonal additivity; inner product space; linear topological space; Tychonoff topology; dense set

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2015
• Tom: 55
• Numer: 2

Daty

wydano

2015

online

2016-05-25

Twórcy

autor

Karol Baron

Identyfikatory

DOI

10.14708/cm.v55i2.1109