Is $\Box_{n\in\omega} \mathbb{R}$ (that is $\mathbb{R}^\omega$ endowed with the box topology) metacompact?
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asked Aug 21, 2018 at 14:03
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4$\begingroup$ Wikipedia says that the box topology on $\mathbb{R}^\omega$ is paracompact if the continuum hypothesis holds and paracompact spaces are metacompact. So under CH the answer is positive. $\endgroup$– James E HansonCommented Aug 21, 2018 at 16:29
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3$\begingroup$ It seems that the paracompactness of the box topology on $\mathbb R^\omega$ can be proved under $\mathfrak b=\mathfrak d$ (which is equivalent to the existence of a scale in $\omega^\omega$). $\endgroup$– Taras BanakhCommented Aug 21, 2018 at 20:44
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3$\begingroup$ @TarasBanakh, Also under $\mathfrak{b}=\aleph_1$ and under $\mathfrak{d}=\mathfrak{c}$. $\endgroup$– Ramiro de la VegaCommented Aug 21, 2018 at 22:30
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