Uniformly locally connected uniform \(\sigma\)-frames
A \(\sigma\)-frame is a \((0,1)\)-lattice with all countable joins satisfying the identity \(x\wedge\bigvee_{y\in Y}y=\bigvee_{y\in Y}(x\wedge y )\) for all coutable sets \(Y\), and homomorphisms are all lattice \((0,1)\)-homomorphisms preserving all countable joins. Many concepts of topological spaces are defined as full subcategories of \(\sigma\)-frames and their relations are studied. Samuel and Stone-Čech compactifications are presented and some of their properties in \(\sigma\)-frames are derived.
scientific article; zbMATH DE number 5651866