Weak covering properties and selection principles

作者：Babinkostova L; Pansera B A; Scheepers M^*

来源：Topology and Its Applications, 2013, 160(18): 2251-2271.

DOI：10.1016/j.topol.2013.07.022

• Productively Menger
• Weakly Menger
• Productively Hurewicz
• Weakly Hurewicz
• Productively Rothberger
• Weakly Rothberger

No convenient internal characterization of spaces that are productively Lindelof is known. Perhaps the best general result known is Alster%26apos;s internal characterization, under the Continuum Hypothesis, of productively Lindelof spaces which have a basis of cardinality at most N-1. It turns out that topological spaces having Alster%26apos;s property are also productively weakly Lindelof. The weakly Lindelof spaces form a much larger class of spaces than the Lindelof spaces. In many instances spaces having Alster%26apos;s property satisfy a seemingly stronger version of Alster%26apos;s property and consequently are productively X, where X is a covering property stronger than the Lindelof property. This paper examines the question: When is it the case that a space that is productively X is also productively Y, where X and Y are covering properties related to the Lindelof property.

• 出版日期2013-12-1