Some remarks on star-Menger spaces using box products
Abstract
This article is a continuation of study of star-Menger selection properties in line of (Ko\v{c}inac, 2009, 2015), where we mainly use covers consisting of $G_\delta$ sets. It is observed that star-Mengerness is equivalent to every such type of covers of a space has a countable subcover.
We improve this result by considering `subcovers of cardinality less than $\mathfrak{b}$' by replacing `countable subcovers', which is our primary observation. We also show that it is possible to produce non normal spaces using box products and dense star-Menger subspaces.
We improve this result by considering `subcovers of cardinality less than $\mathfrak{b}$' by replacing `countable subcovers', which is our primary observation. We also show that it is possible to produce non normal spaces using box products and dense star-Menger subspaces.
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