Tsukuba Journal of Mathematics

On intersections of compacta in Euclidean space: the metastable case

A.N. Dranisnikov, D. Repovs, and E.V. Scepin

Full-text: Open access

Abstract

We prove the following theorem: Let $f:X\rightarrow R^{n}$ and $g:Y\rightarrow R^{n}$ be any maps of compacta $X$ and $Y$ into the Euclidean $n$-space $R^{n}$, $n\geqq 5$. Suppose that $\dim(X\times Y) \lt n$ and that 2 $\dim X+$$\dim Y \lt 2n-1$. Then for every $\epsilon \gt 0$ there exist maps $f^{\prime}$:$X\rightarrow R^{n}$ and $g^{\prime}$:$Y\rightarrow R^{n}$ such that $d(f, f^{\prime}) \lt \epsilon,$d(g, g^{\prime}) \lt \epsilon$ and $f^{\prime}(X)()g^{\prime}(Y)$$=\emptyset$.

Article information

Source
Tsukuba J. Math., Volume 17, Number 2 (1993), 549-564.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496162280

Digital Object Identifier
doi:10.21099/tkbjm/1496162280

Mathematical Reviews number (MathSciNet)
MR1255491

Zentralblatt MATH identifier
0830.54017

Subjects
Primary: 54C25: Embedding 54F45: Dimension theory [See also 55M10] 57Q55: Approximations
Secondary: 55M10: Dimension theory [See also 54F45] 57Q65: General position and transversality

Keywords
Dimension of product of compacta stable intersection of maps metastable range Freudenthal suspension theorem Whitehead products Spanier-Whitehead duality Casson finger moves Cogosvili conjecture regularly branched maps

Citation

Dranisnikov, A.N.; Repovs, D.; Scepin, E.V. On intersections of compacta in Euclidean space: the metastable case. Tsukuba J. Math. 17 (1993), no. 2, 549--564. doi:10.21099/tkbjm/1496162280. https://projecteuclid.org/euclid.tkbjm/1496162280


Export citation