Uniformly continuous extension in $\mathsf{L}$-uniform convergence tower spaces
Abstract
Using an extension theorem for continuous mappings between quantale-valued convergence tower spaces that we obtained in a previous paper, we prove an extension theorem for uniformly continuous mappings between quantale-valued uniform convergence spaces. To this end, we define and study suitable uniform diagonal axioms and uniform regularity for quantale-valued uniform convergence tower spaces.
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