Extensions of Functions and Spaces
Giovanni Viglino · Transactions of the American Mathematical Society · 1973
We investigate, for a given map $\varphi$ from a topological space X to a topological space Y (denoted by $[X,\varphi ,Y]$), those triples $[E,\Phi ,Y]$ where E is an extension of X and $\Phi$ extends $\varphi$ to E. A maximal such extension, similar to the Katětov extension of a topological space, is examined.