Shape morphisms and spaces of approximative maps

Multihomotopy, Čech Spaces of loops and Shape Groups

“…As a result we get a representation of the shape morphisms between X and Y as path-components of the space N(X, Y). Another related representation was given by V. F. Laguna and the author [17] in terms of spaces of approximate maps from X to Y. We also use our notion of multi-net to give an intrinsic description of the shape groups fc n (X, x 0 ) and to define a Cech analogue of the spaces of loops.…”