| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4660661 | Topology and its Applications | 2006 | 7 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
