Abstract:The results concern clopen sets in products of topological spaces. It is shown that a clopen subset of the product of two separable metrizable (or locally compact) spaces is not always a union of clopen boxes. It is also proved that any clopen subset of the product of two spaces, one of which is compact, can always be represented as a union of clopen boxes.
Keywords: clopen set, clopen box, Cartesian product of spaces
AMS Subject Classification: 54B10, 54B15, 55M10