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

نویسندگان
Jager, G. ID 1

1 University of Applied Sciences Stralsund, Stralsund, Germany

doi
10.22111/ijfs.2022.7161
چکیده

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.

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