Homology, Homotopy and Applications

Volume 4 (2002)

Number 1

Topology with monoidal control

Pages: 213 – 234

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n1.a12

Authors

René Depont Christensen (IMADA, Syddansk Universitet, Odense, Denmark)

Hans Jørgen Munkholm (IMADA, Syddansk Universitet, Odense, Denmark)

Abstract

This paper defines monoidal control, which is a specialization of control by entourage as presented in [5]. It is shown that on metric spaces monoidal control generalizes bounded control, and describes continuous control. A systematic way of obtaining results from bounded control, in the sense of [1], as results of monoidal—and hence continuous—control, is developed. Especially this provides versions of the Hurewicz and Whitehead theorems with monoidal control, thus simultaneously establishing them for continuous control over metric spaces.

Keywords

bounded, continuous, entourage, control, monoid, action, category, colimit, Hurewicz

2010 Mathematics Subject Classification

18Exx, 55Uxx

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