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The existence of a connected meager in itself $ \mathsf{CDH}$ space is independent of $ \mathsf{ZFC}$


Authors: Michael Hrušák and Jan van Mill
Journal: Proc. Amer. Math. Soc. 146 (2018), 2689-2695
MSC (2010): Primary 54H05, 03E15, 54E50
DOI: https://doi.org/10.1090/proc/13434
Published electronically: February 28, 2018
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Abstract: We show that the existence of a countable dense homogeneous metric space which is connected and meager in itself is independent of $ \mathsf {ZFC}$.


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Additional Information

Michael Hrušák
Affiliation: Centro de Ciencas Matemáticas, UNAM, A.P. 61-3, Xangari, Morelia, Michoacán, 58089, México
Email: michael@matmor.unam.mx

Jan van Mill
Affiliation: KdV Institute for Mathematics, University of Amsterdam, Science Park 105-107, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: j.vanMill@uva.nl

DOI: https://doi.org/10.1090/proc/13434
Keywords: Countable dense homogeneous, connected, meager
Received by editor(s): May 18, 2016
Received by editor(s) in revised form: August 6, 2016
Published electronically: February 28, 2018
Additional Notes: The first author was supported by a PAPIIT grant IN 108014 and CONACyT grant 177758
The second author is pleased to thank the Centro de Ciencas Matemáticas in Morelia for the generous hospitality and support
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2018 American Mathematical Society

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