Assignments to sheaves of pseudometric spaces

On Pseudometric Spaces 1

The terminology and notation used here have been introduced in the following articles: [9], [4], [13], [12], [10], [8], [2], [3], [1], [14], [7], [11], [5], and [6]. Let M be a metric structure, and let x, y be elements of the carrier of M . The predicate x ≈ y is defined by: (Def.1) ρ(x, y) = 0. Let M be a metric structure, and let x be an element of the carrier of M . The functor x yielding a...

On completeness of quasi-pseudometric spaces

The notion of completeness in metric spaces and that of completing a metric space are traditionally discussed in terms of Cauchy sequences. The main reason being that this concept deals precisely with the issue of convergence of sequences in the sense that every convergent sequence is a Cauchy sequence. The paper deals with completion in a setting that avoids explicit reference to Cauchy sequen...

Sheaves on Spaces 006a

SHEAVES ON SPACES Contents

Sheaves over Topological Spaces

The category of sheaves over a topological space has a rich internal logic, but they also have a very rich geometric interpretation. In these notes I review the basic notions of sheaves over topological spaces, with an emphasis on the geometry of sheaves. I prove that sheaves are toposes, present the proof of the equivalence between the category of sheaves over X and the set of local homeomorph...