Strict T-embeddings

Abstract

The concept of a ⊤-limit space has recently been introduced and studied. It resembles the top level space of a lattice-valued convergence space. In  this context, the notion of a strict T₃-embedding is defined. For a given ⊤-limit space, a connection is made between its strict T₃-compactifications and the set of all totally bounded ⊤- Cauchy spaces which induce the fixed ⊤-limit space and posses a strict T₃-completion.

Key words: Lattice-valued convergence, ⊤-compactifications, ⊤-completions, ⊤-filters, ⊤-ultrafilters.