Singular sets and remainders

Nonhomogeneity of Remainders, Ii

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...

Stability Modulus Singular Sets

A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of Cr endomorphisms with singularities. A map that is stable in this sense will be conjugated to each perturbation that is equivalent to it in a geometric sense. It will be shown that this kind of stability implies Axiom A, Omega-stability and that every critical point is wanderin...

y-SETS AND OTHER SINGULAR SETS OF REAL NUMBERS

In the papers of Gerlits-Nagy [4] and McCoy [6] a study is made of properties of a space X which imply or are equivalent to other properties of the space C(X) (i.e. space of continuous real-valued functions on X with the topology of pointwise convergence). A family 2 of open subsets of X is an w-cover of X iff every finite subset of X is contained in an element of 9. A space X has the y-propert...

Singular sets of Sobolev functions

Singular Value Decomposition Geršgorin Sets

Abstract: In this note, we introduce the singular value decomposition Geršgorin set, Γ (A), of an N ×N complex matrix A, where N ≤ ∞. For N finite, the set Γ (A) is similar to the standard Geršgorin set, Γ(A), in that it is a union of N closed disks in the complex plane and it contains the spectrum, σ(A), of A. However, Γ (A) is constructed using column sums of singular value decomposition matr...