On polynomial generators in the algebra of complex functions on a compact space

Gabriel Katz

Vol. 121 (1986), No. 1, 83–92

DOI: 10.2140/pjm.1986.121.83

Abstract

In this paper we prove that in the space of all continuous mappings of a k-dimensional compact space X into complex linear space Cⁿ the imbeddings F : X → Cⁿ with the property “any complex continuous function on F(X) can be uniformly approximated by complex polynomials on Cⁿ” form a dense subset of type G_δ, provided that k ≤n.

Mathematical Subject Classification 2000

Primary: 46E25

Secondary: 32E30, 54C05

Milestones

Received: 28 June 1984

Revised: 3 February 1985

Published: 1 January 1986