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.

کلیدواژه ها:

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