Witold Marciszewski: On zero-dimensional subspaces of Eberlein compacta
12/04/21 17:02
Tuesday, April 13, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Witold Marciszewski (University of Warsaw)
Title: On zero-dimensional subspaces of Eberlein compacta
Abstract: Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. Our talk will be devoted to the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. Several such spaces were obtained using some additional set-theoretic assumptions. Recently, P. Koszmider constructed the first such example in ZFC. We investigate this problem for the class of Eberlein compact spaces. We construct such Eberlein compacta, assuming the existence of a Luzin set. We also show that it is consistent with ZFC that each Eberlein compact space of weight greater than \(\omega_1\) contains a nonmetrizable closed zero-dimensional subspace.
The talk is based on the paper "On two problems concerning Eberlein compacta": http://arxiv.org/abs/2103.03153
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Witold Marciszewski (University of Warsaw)
Title: On zero-dimensional subspaces of Eberlein compacta
Abstract: Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. Our talk will be devoted to the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. Several such spaces were obtained using some additional set-theoretic assumptions. Recently, P. Koszmider constructed the first such example in ZFC. We investigate this problem for the class of Eberlein compact spaces. We construct such Eberlein compacta, assuming the existence of a Luzin set. We also show that it is consistent with ZFC that each Eberlein compact space of weight greater than \(\omega_1\) contains a nonmetrizable closed zero-dimensional subspace.
The talk is based on the paper "On two problems concerning Eberlein compacta": http://arxiv.org/abs/2103.03153