On orthogonally additive injections and surjections

Karol 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 -