Geodesic
On clopen sets in Cartesian products
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 357-362.

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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.
Classification : 54B10, 54B15, 54D20, 54H05, 55M10
Keywords: clopen set; clopen box; Cartesian product of spaces 
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     title = {On clopen sets in {Cartesian} products},
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Buzyakova, Raushan Z. On clopen sets in Cartesian products. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 2, pp. 357-362. http://geodesic.mathdoc.fr/item/CMUC_2001__42_2_a12/