## On linear operators and functors extending pseudometrics

### Volume 142 / 1993

Fundamenta Mathematicae 142 (1993), 101-122
DOI: 10.4064/fm-142-2-101-122

#### 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.