On linear operators and functors extending pseudometrics

C. Bessaga

Fundamenta Mathematicae (1993)

  • Volume: 142, Issue: 2, page 101-122
  • ISSN: 0016-2736

Abstract

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For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces, then continuous linear operators extending metrics always exist.

How to cite

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Bessaga, C.. "On linear operators and functors extending pseudometrics." Fundamenta Mathematicae 142.2 (1993): 101-122. <http://eudml.org/doc/211975>.

@article{Bessaga1993,
abstract = {For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces, then continuous linear operators extending metrics always exist.},
author = {Bessaga, C.},
journal = {Fundamenta Mathematicae},
keywords = {squeezed cones; metrizable topological space},
language = {eng},
number = {2},
pages = {101-122},
title = {On linear operators and functors extending pseudometrics},
url = {http://eudml.org/doc/211975},
volume = {142},
year = {1993},
}

TY - JOUR
AU - Bessaga, C.
TI - On linear operators and functors extending pseudometrics
JO - Fundamenta Mathematicae
PY - 1993
VL - 142
IS - 2
SP - 101
EP - 122
AB - For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces, then continuous linear operators extending metrics always exist.
LA - eng
KW - squeezed cones; metrizable topological space
UR - http://eudml.org/doc/211975
ER -

References

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