The order structure of Wallman nearnesses (Q1323272)

Nearness structures are known to form an elegant tool for the investigtation of strict \(T_ 1\)-extensions of topological \(T_ 1\)- spaces \(X\). In particular for a given \(T_ 1\)-space \(X\), compatible concrete nearness structures correspond naturally to strict \(T_ 1\)- extensions of \(X\), and compatible Wallman-nearness structures correspond to Wallman-type extensions of \(X\). The ordered collection of all compatible concrete nearness structures on \(X\) is known to be a complete lattice \(L(X)\). In the paper under review the authors demonstrate that the ordered subset of \(L(X)\), consisting of all Wallman-nearness structures, is a complete lattice in its own right, but may fail to be closed under the formation of least upper bounds in \(L(X)\).