Recent progress on characterizing lattices C(X) and U(Y )
Miroslav Hus̆ek, Antonio Pulgarín · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 2013
Our effort to weaken algebraic assumptions led us to obtain characterizations of C(X) as Riesz spaces, real l-groups, semi-affine lattices and real lattices by using different techniques. We present a unified approach valid for any “convenient” category. By setting equivalent conditions to equi-uniform continuity, we obtain a characterization of the lattice U(Y ) in parallel with that of C(X).