Dimension and superposition of continuous functions

Michael Levin

doi:10.1007/BF02807868

Dimension and superposition of continuous functions

Michael Levin

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We give a relatively short proof of the following theorem of Sternfeld: Let X be a compact metric space with dim X ≧ 2, and let X ⊂R^m be an embedding such that every f ∈C(X) can be represented as {Mathematical expression} Then m ≧ 2 dim X + 1.

Original language	English
Pages (from-to)	205-218
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1007/BF02807868
State	Published - 1 Jun 1990
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF02807868

Cite this

@article{89d64611c61e44318849f5fc7024dec1,

title = "Dimension and superposition of continuous functions",

abstract = "We give a relatively short proof of the following theorem of Sternfeld: Let X be a compact metric space with dim X ≧ 2, and let X ⊂R m be an embedding such that every f ∈C(X) can be represented as {Mathematical expression} Then m ≧ 2 dim X + 1.",

author = "Michael Levin",

year = "1990",

month = jun,

day = "1",

doi = "10.1007/BF02807868",

language = "English",

volume = "70",

pages = "205--218",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Dimension and superposition of continuous functions

AU - Levin, Michael

PY - 1990/6/1

Y1 - 1990/6/1

N2 - We give a relatively short proof of the following theorem of Sternfeld: Let X be a compact metric space with dim X ≧ 2, and let X ⊂R m be an embedding such that every f ∈C(X) can be represented as {Mathematical expression} Then m ≧ 2 dim X + 1.

AB - We give a relatively short proof of the following theorem of Sternfeld: Let X be a compact metric space with dim X ≧ 2, and let X ⊂R m be an embedding such that every f ∈C(X) can be represented as {Mathematical expression} Then m ≧ 2 dim X + 1.

UR - http://www.scopus.com/inward/record.url?scp=51249173348&partnerID=8YFLogxK

U2 - 10.1007/BF02807868

DO - 10.1007/BF02807868

M3 - Article

AN - SCOPUS:51249173348

SN - 0021-2172

VL - 70

SP - 205

EP - 218

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Dimension and superposition of continuous functions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this