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On basic embeddings of compacta into the plane

Published online by Cambridge University Press:  17 April 2009

Neža Mramor-Kosta  and
Eva Trenklerová
Neža Mramor-Kosta
Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia, e-mail: neza.mramor-kosta@fri.uni-lj.si
Eva Trenklerová
Affiliation:
Faculty of Science, P. J. Šafárik University Košice, Slovakia, e-mail: etrenkle@cs.science.upjs.sk
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Abstract

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A compactum K ⊂ ℝ2 is said to be basically embedded in ℝ2 if for each continuous function f: K → ℝ there exist continuous functions g, h: ℝ → ℝ such that f(x, y) = g(x) + h(y) for each point (x, y) ∈ K. Sternfeld gave a topological characterization of compacta K which are basically embedded in ℝ2 which can be formulated in terms of special sequences of points called arrays, using arguments from functional analysis. In this paper we give a simple topological proof of the implication: if there exists an array in K of length n for any n ∈ ℕ, then K is not basically embedded.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 471 - 480
Copyright
Copyright © Australian Mathematical Society 2003

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