DOIAbstract
AbstractWe present a new version of Šapirovskiı̆'s well-known criterion for the existence of a continuous mapping from a compactum onto a Tychonoff cube. From this, we prove that under MA for every compact Hausdorff space X of weight less than 2ℵ0 and every infinite cardinal τ<2ℵ0 the following conditions are equivalent: 1. there exists a continuous surjection from X onto the Tychonoff cube Iτ;2. there exists a continuous injection from the Cantor cube Dτ into X;3. there exists a closed subset Y⫅X such that χ(y,Y)≥τ for any y∈Y.
Add to ORKG