Coarse metric and uniform metric

Metric–fine uniform frames

A locallic version of Hager’s metric-fine spaces is presented. A general definition of A-fineness is given and various special cases are considered, notably A = all metric frames, A = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Metric Spaces and Uniform Structures

The general notion of topology does not allow to compare neighborhoods of different points. Such a comparison is quite natural in various geometric contexts. The general setting for such a comparison is that of a uniform structure. The most common and natural way for a uniform structure to appear is via a metric, which was already mentioned on several occasions in Chapter 1, so we will postpone...

metric frames

dar in paian name dar ebteda mafahim topologicy baian mishavad va sepas mafahim rastehie va frames ha ra baian mikonim

Uniform Domains and the Quasi-hyperbolic Metric

The Coarse Geometry of the Teichmüller Metric

We study the coarse geometry of the Teichmüller space of a compact surface in the Teichmüller metric. We show that this admits a ternary operation, natural up to bounded distance, which endows the space with the structure of a coarse median space whose rank is equal to the complexity of the surface. We deduce that Teichmüller space satisfies a coarse quadratic isoperimetric inequality. We descr...