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

Document Type : Research Paper


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.


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