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Products of k -spaces, and questions

Yoshio Tanaka (2003)

Commentationes Mathematicae Universitatis Carolinae

As is well-known, every product of a locally compact space with a k -space is a k -space. But, the product of a separable metric space with a k -space need not be a k -space. In this paper, we consider conditions for products to be k -spaces, and pose some related questions.

Products of Lindelöf T 2 -spaces are Lindelöf – in some models of ZF

Horst Herrlich (2002)

Commentationes Mathematicae Universitatis Carolinae

The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...

Products of non- σ -lower porous sets

Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

In the present article we provide an example of two closed non- σ -lower porous sets A , B such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A X be a non- σ -lower porous Suslin set and let B Y be a non- σ -porous Suslin set. Then the product A × B is non- σ -lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non- σ -lower porous sets in topologically...

Products of topological spaces and families of filters

Paolo Lipparini (2023)

Commentationes Mathematicae Universitatis Carolinae

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by ω 1 factors are Lindelöf. Parallel results are obtained for final ω n -compactness, [ λ , μ ] -compactness, the Menger and the Rothberger properties.

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