On basic embeddings of compacta into the plane
2003 ◽
Vol 68
(3)
◽
pp. 471-480
Keyword(s):
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.
1967 ◽
Vol 10
(3)
◽
pp. 361-364
◽
2021 ◽
Vol 7
(1)
◽
pp. 88-99
2007 ◽
Vol 62
(5)
◽
pp. 173-180
1985 ◽
Vol 260
(16)
◽
pp. 9137-9145
Keyword(s):
2016 ◽
Vol 15
(08)
◽
pp. 1650149
◽
Keyword(s):