Products of Menger spaces in the Miller model

Abstract

We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and combinatorial covering properties in topology.

arXiv admin note: text overlap with arXiv:1712.03899

References in corpus (4)

• A semifilter approach to selection principles
• On M-separability of countable spaces and function spaces
• Products of Menger spaces: a combinatorial approach
• Products of Hurewicz spaces in the Laver model

Cited by in corpus (4)

• On Traditional Menger and Rothberger Variations
• M-separable spaces of functions are productive in the Miller model
• Coideals as remainders of groups distinguishing between combinatorial covering properties
• Preservation of $\gamma$-spaces and covering properties of products