It is easy to see that every open cover of the square of a metrizable space X can be refined by the square of an open cover of X iff X is either compact, or discrete. We consider what happens if metrizability is dropped, as well as some modifications of the statement above, in particular those involving covers by stars. Several questions are posed.
WHEN CAN A COVER OF A PRODUCT BE REFINED BY A PRODUCT OF COVERS?
Pansera, Bruno Antonio
2008-01-01
Abstract
It is easy to see that every open cover of the square of a metrizable space X can be refined by the square of an open cover of X iff X is either compact, or discrete. We consider what happens if metrizability is dropped, as well as some modifications of the statement above, in particular those involving covers by stars. Several questions are posed.File in questo prodotto:
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