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Assuming the continuum hypothesis, a normal nonmetrizable Moore space is constructed. This answers a question raised by F. B. Jones in 1931, using an axiom well known at that time. For the construction, a consequence of the continuum hypothesis that also follows from the nonexistence of an inner model with a measurable cardinal is used. Hence, it is shown… (More)
The central box product problem states: Given the box topology, is the product of countably many copies of the real line a normal space? In the first part of this paper, we survey recent results we believe related to the central problem. In the second part of this paper we present interesting additional open problems about box products related to the… (More)
We prove that paranormal spaces of character ≤ ω 1 are ω 1-collectionwise Hausdorff assuming the set-theoretic principle ♦ *. This gives an affirmative answer to problem 197 in Problems I wish I could solve, by W.
Note there are many papers where box products are an important yet a secondary topic (for example Rudin's solution to the Dowker problem, Dow's A Separable Space with no Remote Points, or Vaughan's Products of ω µ-metrizable spaces) are not included here. 1. Box products and the axiom of choice. [Boxprodukte undAuswahlaxiom (in German)] 2. The box product… (More)