Topological group foundations of rigid space geometry

Foundations of Differential Geometry

These notes are from a lecture course Di erentialgeometrie und Lie Gruppen which has been held at the University of Vienna during the academic year again in and in WS It is not yet complete and will be enlarged during the year In this lecture course I give complete de nitions of manifolds in the beginning but beside spheres examples are treated extensively only later when the theory is develope...

Lattice of compactifications of a topological group

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

Topological Foundations of Cognitive Science

1. The Concept of Transformation A first introduction to the basic concepts of topology takes as its starting point the notion of transformation. We note, familiarly, that we can transform a spatial body such as a sheet of rubber in various ways which do not involve cutting or tearing. We can invert it, stretch or compress it, move it, bend it, twist it, or otherwise knead it out of shape. Cert...

Algebraic Geometry Foundations

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...