Geodesic
Topology with monoidal control
Homology, homotopy, and applications, Tome 4 (2002) no. 1, pp. 213-234.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2002.v4.n1.a12
Classification : 18Exx, 55Uxx
Keywords: bounded, continuous, entourage, control, monoid, action, category, colimit, Hurewicz 
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René Depont Christensen; Hans Jørgen Munkholm. Topology with monoidal control. Homology, homotopy, and applications, Tome 4 (2002) no. 1, pp. 213-234. doi : 10.4310/HHA.2002.v4.n1.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2002.v4.n1.a12/

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