We introduce an endofunctor H on the category baℓ of bounded archimedean ℓ-algebras and show that there is a dual adjunction between Alg(H) algebras for Coalg(V) coalgebras Vietoris V compact Hausdorff spaces. prove Gelfand duality lifts to equivalence full reflective subcategory Algu(H) Alg(H). provide alternate view by introducing Hu consisting uniformly complete objects showing Alg(Hu) isomo...

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ-complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

A ring of continuous functions is a ring of the form C(X), the ring of all continuous real-valued functions on a completely regular Hausdorff space X. With each ideal / of C(X), we associate certain subalgebras of C(X), and discuss their structure spaces. We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces. Introducti...

This paper is a continuation of work done by the present author together with P. R. Hall [1]. We characterise the prime and equiprime radicals of N0(G) for certain topological groups G. Various results are obtained concerning primeness and strongly primeness for the sandwich near-ring N0(G,X, θ). MSC 2000: 16Y30, 22A05

1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...