Some new continuation theorems are presented for admissible (and more general) maps using the idea of extendability. In this paper we use the notion of extendability to establish new continuation theorems for admissible (and more general) maps. The ideas used are elementary, in particular the notion of homotopy and Urysohn functions. An added bonus is that the results hold for maps between Hausdorff topological spaces (i.e. the spaces need not be vector spaces). Our theory was motivated by the books [2, 3] and the references therein.
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