We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

Let $G$ be a group and $A$ a set. A cellular automaton (CA) $\tau$ over $A^G$ is von Neumann regular (vN-regular) if there exists a CA $\sigma$ over $A^G$ such that $\tau \sigma\tau = \tau$, and in such case, $\sigma$ is called a generalised inverse of $\tau$. In this paper, we investigate vN-regularity of various kinds of CA. First, we establish that, over any nontrivial configuration space, t...

In this paper, we study the construction of irregular shearlet systems, i.e., systems of the form SH(ψ,Λ) = {a− 4 ψ(A−1 a S−1 s (x− t)) : (a, s, t) ∈ Λ}, where ψ ∈ L(R), Λ is an arbitrary sequence in R ×R×R2, Aa is a parabolic scaling matrix and Ss a shear matrix. These systems are obtained by appropriately sampling the Continuous Shearlet Transform. We derive sufficient conditions for such a d...

Let = (X,R) be a distance-regular graph of diameter d . A parallelogram of length i is a 4-tuple xyzw consisting of vertices of such that ∂(x, y)= ∂(z,w)= 1, ∂(x, z)= i, and ∂(x,w)= ∂(y,w)= ∂(y, z)= i− 1. A subset Y of X is said to be a completely regular code if the numbers πi,j = | j (x)∩ Y | (i, j ∈ {0,1, . . . , d}) depend only on i = ∂(x,Y ) and j . A subset Y of X is said to be strongly c...