Equi-isoclinic subspaces of Euclidean spaces

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...

Subspaces of Knot Spaces

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

Subspaces of pseudoradial spaces

We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1-space). This answers the Problem 3 in [2]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top.

Almost Euclidean Quotient Spaces of Subspaces of a Finite-dimensional Normed Space

The main result of this article is Theorem 1 which states that a quotient space Y, dim Y = k, of a subspace of any finite dimensional normed space X, dim X — n, may be chosen to be J-isomorphic to a euclidean space even for k = [Xn] for any fixed X < 1 (and d depending on X only). The following theorem is proved. 1. Theorem. For every d > 1 there exists X(d) > 0 such that every n-dimensional no...

ε-weakly Chebyshev subspaces and quotient spaces