The Normal Completion of the Lattice of Continuous Functions
R. P. Dilworth · Birkhäuser Boston eBooks · 1990
Let S be a topological space( 1 ) and let C ( S ) denote the set of all real valued, bounded, continuous functions on S . It is well known that C ( S ) is a distributive lattice under the operations sup ( f,g ) and inf ( f,g ). In general, however, C ( S ) is not a complete lattice; that is, an arbitrary bounded set of continuous functions in C ( S ) need not have a least upper bound in the lattice C ( S ). Furthermore, the structure of the minimal completion of C ( S ) by means of normal subsets has not been determined even in the simple case where S is the real interval [0, 1]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.