We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomor-phic to the measure algebra of 2 ! 1. The rst construction uses } to produce an S-space with no convergent sequences in which every perfect set is a G. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The sec...

It is shown that every Radon measure on a first-countable Hausdorff space is separable provided ω1 is a precaliber of every measurable algebra. As the latter is implied by MA(ω1), the result answers a problem due to D. H. Fremlin. Answering the problem posed by D. H. Fremlin ([4], 32R(c)), we show in this note that, assuming (∗) ω1 is a precaliber of every measurable Boolean algebra, every Rado...

In addition to its expected fast, additive L- and M-cone inputs (L + M), the luminance pathway has slow, spectrally opponent inputs. We have previously shown that on long-wavelength fields, the dominant slow signals change from L-M at moderate intensity levels to M-L signals at high. Here, we focus on the transition between them, which we find is marked by substantial changes in temporal phase ...

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C∗algebras: (i) Jiang-Su stability, (ii) unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C∗-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C∗-algebra whos...

Let A be a separable C−algebra and A its enveloping W −algebra. A result of Akemann, Anderson, and Pedersen states that if {pn} is a sequence of mutually orthogonal, minimal projections in A such that P ∞ k pn is closed, ∀k, then there is a MASA B in A such that each φn|B is pure and has a unique state extension to A, where φn is the pure state of A supported by pn. We generalize this result in...

We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An algebra RFD while simultaneously possessing completely isometric representations whose generating C⁎-algebra is RFD. This has provided many hurdles in characterizing residual finite-dimensionality for algebras. To better understand the elusive behavior, we explore C⁎-covers of an algebra. First, ...

Introduction. It has been shown in a previous paper [3]1 that every algebra A with radical R, such that A/R is separable, is a homomorphic image of a certain maximal algebra which is determined to within an isomorphism by A/R, the A/R-modu\e (two-sided) R/R1, and the index of nilpotency of R. Furthermore, some indication was given of how the structure of maximal algebras can be determined in si...

Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary 2-category. Examples include G-graded fusion 1-categories, G-crossed 1-categories. explore the properties 2-categories modules bimodules over algebra, by giving criterion for existence right left adjoints. Then, we co...