A metrization problem concerning lattices

The Metrization Problem for Fréchet Groups

In this article, we will be interested in the extent to which the assumption of first countability in this theorem can be weakened. Recall that a Hausdorff topological space X is Fréchet if whenever x is a limit point of A ⊆ X, there is a sequence an (n < ω) of elements of A which converges to x. This is a natural weakening of first countability which has been extensively studied in the literat...

A Reflexivity Problem concerning The

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

On the Metrization Problem and Related Problems In

Nagata-Smirnov Metrization Theorem.nb

Introduction: The Nagata-Smirnov Metrization theorem gives a full characterization of metrizable topological spaces. In other words, the theorem describes the necessary and sufficient conditions for a topology on a space to be defined using some metric. As a motivational example, consider the discrete topology on some space (every subset of the space is open). Though it might not be apparent to...

Channel Metrization

We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder. We also show that any metric, up to a decoding equivalence, can be isometrically embedded into the hypercube with the Hamming metric, and thus, in terms of decoding, the Hamming metric is universal. keywords: Coding Theory;...