G. Jager - University of Applied Sciences Stralsund, Stralsund, Germany

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.

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