A homogeneous space whose complement is rigid

A Homogeneous Space Whose Complement Is Rigid

We construct a homogeneous subspace of 2ω whose complement is dense in 2ω and rigid. Using the same method, assuming Martin’s Axiom, we also construct a countable dense homogeneous subspace of 2ω whose complement is dense in 2ω and rigid.

The Complement of a D-Tree is Pure Shellable

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...

A Point Set Whose Space of Triangulations Is Disconnected

In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is an isolated element in the graph of triangulations of the point configuration. It has been a central open question in polytope combinatorics in the last decade whether point configurations exist for...

A Rigid Space Homeomorphic to Hilbert Space

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on `2, and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorp...