On products of discretely generated spaces |
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Authors: | Eva Murtinová |
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Affiliation: | Charles University, Faculty of Mathematics and Physics, Department of Math. Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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Abstract: | Assuming a measurable cardinal exists, we construct a pair of discretely generated spaces whose product fails to be weakly discretely generated. Under the Continuum Hypothesis, a similar result is obtained for a pair of countable Fréchet spaces as well as for two compact discretely generated spaces whose product is not discretely generated. A somewhat weaker example is presented assuming Martin's Axiom for countable posets. Further, the class of strongly discretely generated compacta is shown to preserve discrete generability in products. |
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Keywords: | 54A35 54B10 54G20 |
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