arXiv subjects
Publications and source records attributed to Stephen Semmes.
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
Here we look at some geometric properties related to connectedness and topological dimension 0, especially in connection with norms on vector spaces over fields with absolute value functions, which may be non-archimedian.
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
A field with an absolute value function is a basic type of metric space, which includes the real and complex numbers with their standard metrics, and ultrametrics on fields like the p-adic numbers. Here we try to give some perspectives of analysis in situations like these.
Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
It is well known that n x n upper-triangular real matrices with 1's on the diagonal form a nilpotent Lie group with an interesting family of non-isotropic dilations and corresponding geometry, as in [9]. Here we look at p-adic versions of this, and related matters.
A basic class of constructions is considered, in connection with bilipschitz mappings in particular.
A class of solenoids is considered, including some aspects in n (topological) dimensions, where one basically gets some fractal versions of tori.
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
Here we look at some related constructions of solenoids, and mappings associated to them.
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
In these informal notes, we continue to explore p-adic versions of Heisenberg groups and some of their variants, including the structure of the corresponding Cantor sets.
These informal notes deal with p-adic versions of Heisenberg groups and related matters.
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.