Transversal intersection formula for compacta

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 ∩ Y) ⩾ dim(X × Y) − n for transversally intersecting compacta X, Y ⊂ Rn, based on a correct interpretation of the classical Čogošvili theorem. Also included is a short summary of a new direction of dimension theory, called extension theory, which is needed for the proof.