On the extension of mappings in Stone-Weierstrass spaces

Abstract

N. Veličko generalized the well-known result of A. D. Taĭmanov on the extension of continuous functions by showing that Taĭmanov’s theorem holds when Y Y (the image space) is H H -closed and Urysohn and the mapping f f is weakly θ \theta -continuous. We obtain, in a more direct fashion, an even stronger generalization of this theorem. We proceed to show that the class of all SW spaces is not reflective in the category of all completely Hausdorff spaces and continuous mappings. However, an epi-reflective situation is achieved by suitably enlarging the class of admissible morphisms. We conclude by establishing a number of results about SW extension spaces.