# On orthogonally additive injections and surjections

Commentationes Mathematicae (2015)

- Volume: 55, Issue: 2
- ISSN: 2080-1211

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topKarol Baron. "On orthogonally additive injections and surjections." Commentationes Mathematicae 55.2 (2015): null. <http://eudml.org/doc/292400>.

@article{KarolBaron2015,

abstract = {Let $E$ be a real inner product space of dimension at least 2 and $V$ a linear topological Hausdorff space. If $\operatorname\{card\}E\le \operatorname\{card\} V$, 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 $\operatorname\{card\}V\le \operatorname\{card\}E$, 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.},

author = {Karol Baron},

journal = {Commentationes Mathematicae},

keywords = {orthogonal additivity; inner product space; linear topological space; Tychonoff topology; dense set},

language = {eng},

number = {2},

pages = {null},

title = {On orthogonally additive injections and surjections},

url = {http://eudml.org/doc/292400},

volume = {55},

year = {2015},

}

TY - JOUR

AU - Karol Baron

TI - On orthogonally additive injections and surjections

JO - Commentationes Mathematicae

PY - 2015

VL - 55

IS - 2

SP - null

AB - Let $E$ be a real inner product space of dimension at least 2 and $V$ a linear topological Hausdorff space. If $\operatorname{card}E\le \operatorname{card} V$, 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 $\operatorname{card}V\le \operatorname{card}E$, 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.

LA - eng

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

UR - http://eudml.org/doc/292400

ER -

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