The main result of this paper is a generalization of a theorem of R. S. Phillips [6] on the nonexistence of projections of l°° onto c0. If S is a locally compact Hausdorff space then let C(S) denote the space of bounded continuous real (or complex) valued functions on 5; also, let Co(S) be those functions in C(S) which vanish at infinity. If N is the space of positive integers with the discrete...

In a classic paper, Smirnov [14] characterized the poset of compactifications of a completely regular space in terms of the proximities on the space. Later, Smyth [15] introduced the notion of a stable compactification of a T0-space and described them in terms of quasi-proximities on the space. Banaschewski [1] formulated Smirnov’s results in the pointfree setting, defining a compactification o...

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...