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Transversal intersection formula for compacta. (English) Zbl 0958.55001
Summary: The main purpose of this paper is to present a unified treatment of the formula for dimension of the transversal intersection of compacta in Euclidean spaces. A new contribution is the proof of inequality \(\dim(X\cap Y)\geq\dim (X\times Y)-n\) for transversally intersecting compacta \(X,Y\subset \mathbb{R}^n\), based on a correct interpretation of the classical Chogoshvili theorem [G. S. Chogoshvili, Compos. Math. 5, 292-298 (1937; Zbl 0018.09103)]. Also included is a short summary of a new direction of dimension theory, called extension theory, which is needed for the proof.

MSC:
55M10 Dimension theory in algebraic topology
54F45 Dimension theory in general topology
Citations:
Zbl 0018.09103
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