Lattice-valued semiuniform convergence spaces (Q1759630)

The author studies two extensions of the category of semiuniform convergence spaces, namely the categories \(SL\)-\textbf{SUConv} of stratified \(L\)-semiuniform convergence spaces and \(SL\)-\textbf{OSUConv} of stratified \(L\)-ordered semiuniform convergence spaces, where \(L\) denotes an arbitrary complete Heyting algebra. It is shown that (i) \(SL\)-\textbf{SUConv} is topological; (ii) \(SL\)-\textbf{OSUConv} is a bireflective full subcategory of \(SL\)-\textbf{SUConv}, and hence it is topological; (iii) both categories are Cartesian-closed; (iv) \(SL\)-\textbf{SUConv} is extensional; (v) both categories are closed under the formation of products of quotient mappings.