This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that (i) the epicomplete metric frames are uniquely determined by the power-set lattices of sets, (ii) episurjective is the same as Boolean, (iii) a metric frame has an epicompletion iff it is spatial, and (iv) the subcategory of epicomplete L in ...

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...

By Gelfand-Neumark duality, the category C∗Alg of commutative C∗algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category uba` of uniformly complete bounded Archimedean `-algebras. Consequently, C∗Alg is equivalent to uba`, and this equivalence can be described through complexification. In this article we study u...

For a subset A of an -group B, r(A,B) denotes the relative uniform closure of A in B. RX denotes the -group of all real-valued functions on the set X, and when X is a topological space, C∗(X) is the -group of all bounded continuous real-valued functions, and B(X) is the -group of all Baire functions. We show that B(X) = r (C∗(X), B(X)) = r ¡ C∗(X), R ¢ . This would appear to be a purely order-t...

 The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...

In this article the frame-theoretic account of what is archimedean for order-algebraists, and semisimple for people who study commutative rings, deepens with the introduction of J -frames: compact normal frames that are join-generated by their saturated elements. Yosida frames are examples of these. In the category of J -frames with suitable skeletal morphisms, the strongly projectable frames a...