For a compact set E with connected complement in the com plex plane we consider a problem of the uniform approximation on E by the weighted polynomials W z Pn z where W z is a continuous non vanishing weight function on E analytic in the interior of E Let A E W be the set of functions uniformly approximable on E by such weighted polynomials If E has empty interior then A E W is completely char ...

We investigate the structure of Gδ ideals of compact sets. We define a class of Gδ ideals of compact sets that, on the one hand, avoids certain phenomena present among general Gδ ideals of compact sets and, on the other hand, includes all naturally occurring Gδ ideals of compact sets. We prove structural theorems for ideals in this class, and we describe how this class is placed among all Gδ id...

In this paper we study sets of surfaces which are isospectral with respect to the Laplace-Beltrami operator. More specifically, for closed surfaces (compact, no boundary) we consider a fixed surface and the family of metrics on that surface having a given Laplace spectrum, whereas for surfaces with boundary we confine our study to the class of simply connected planar domains all having the same...

In the ideal topological spaces (X, ?, I) and (Y, J, ?), we define (I, J)-irresolute function, weakly-(I, J)-irresolute, strongly-(I, functions, semi-I-open sets quasi-H-closed modulo I. We discuss properties of function mapping connected, closed, compact I semi-I-isolated points. J)-Homeomorphisim on presemi-I-open closure subsets are explored in this paper.

The solvability of the Hausdorff moment problem for an arbitrary compact subset of Euclidean n-space is shown to be equivalent to the nonnegativity of a family of quadratic forms derived from the given moment sequence and the given compact set. A variant theorem for the one-dimensional case and an analogous theorem for the trigonometric moment problem are also given. The one-dimensional theorem...