On intersections of compacta of complementary dimensions in Euclidean space
- Dranišnikov, A.N.
- Repovš, D.
- Ščepin, E.V.
Publication date
March 1991
DOI Publisher
Published by Elsevier B.V. ISSN
0166-8641 Citation count (estimate)
36Abstract
AbstractA pair of maps f:X → Rn and g: Y → Rn of compacta X and Y into the Euclidean n-space is said to have a stable intersection if there exist ε>0 such that for any other pair of maps f′:X → Rn and g′:Y → Rn, satisfying ρ(f,f′) <ε and ρ(g,g′)<ε, it follows that f′(X) ∩ g′(Y) ≠ 0. The main result of this paper is the following theorem: Let X and Y be compacta and let n = dim X + dim Y. Then there exists a pair of maps f:X → Rn and g:Y → Rn with stable intersection if and only if dim(X × Y) = n
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