Abstract
1. Introduction. It is known (6) that the connectivity conditions on the manifolds in Irwin's embedding theorem (7) can be replaced by a connectivity condition on the map. This has led to the suggestion that in Hudson's analogue of Irwin's theorem for bounded manifolds (5), (6), the connectivity conditions on the manifolds modulo boundary can be replaced by the corresponding connectivity condition on the map modulo boundary. The main purpose of the present note is to show that this is in fact false, as is the formal analogue of Irwin's and Hudson's theorems for manifold triads. Its other purpose is to announce a related embedding theorem for manifolds with boundary which appeared in (3).
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