Diagonal conditions and uniformly continuous extension in \top-uniform limit spaces

We study suitable diagonal conditions for \top-uniform limit spaces. A dual diagonal condition is shown to be a suitable axiom for uniform regularity. We characterize this regularity concept by closures of L-sets. We apply all these diagonal axioms and prove an extension theorem for uniformly continuous mappings defined on a dense subspace.

Keywords:

topology , top-filter , uniform limit space , lattice-valued uniform convergence space , probabilistic uniform space , diagonal axiom , uniform regularity , extension of mappings