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Topology with Monoidal Control

René dePont Christensen and Hans Jörgen Munkholm

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 continouos-, control, is developed. Especially this provides versions of the Hurewicz and Whitehead theorems with monoidal control, thus simultaneously establishing them for continouos control over metric spaces.

Homology, Homotopy and Applications, Vol. 4(2002), No. 1, pp. 213-234

http://www.rmi.acnet.ge/hha/volumes/2002/n1a12/v4n1a12.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2002/n1a12/v4n1a12.dvi (ps, dvi.gz, ps.gz, pdf)