Let CΨ (X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ (X) is pure if and only if βX−kX is a round subset of βX, CΨ (X) is a projective C(X)-module if and only if CΨ (X) is pure and kX is paracompact. We also show that if CΨ (X) is pure, then for each f ∈ CΨ (X) the ideal (f ) is a projective (flat)...

The construction of an input-to-state stability (ISS) Lyapunov function for networks of ISS system will be presented. First we construct ISS Lyapunov functions for each strongly connected component, then what remains is a cascade (or disconnected aggregation) of these strongly connected components. Using known results the constructed Lyapunov functions can be aggregated to one single ISS Lyapun...

In this paper, we study MV?algebra of continuous functions C(X) and maximal ideals C(X). Furthermore, Z?ideal Z??ideal are introduced proved that every in is a but the converse not true finitely generated basic Z??ideal. Also, investigate meet join two Z?ideals (Z??ideal) Complemented elements examined their properties have been studied. particular, relationship between ideal by them (Z??ideals...

G always denotes an archimedean `-group. We call G epicomplete if G is divisible, -complete, and laterally -complete. X always denotes a Tychono¤ space. D (X ) is the set of continuous f : X ! [ 1;+1] with f 1 (( 1;+1)) dense. It is familiar and useful that every G has representations in various D (X ) : It is known that (A) G is epicomplete with weak unit e if and only if there is a compact ba...