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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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When do connected spaces have nice connected preimages?
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by Vladimir V. Tkachuk PDF
Proc. Amer. Math. Soc. 126 (1998), 3437-3446 Request permission

Abstract:

We prove that every connected Tychonoff space is an open monotone continuous image of a connected strictly $\sigma$-discrete left-separated Tychonoff space. For wide classes of connected spaces it is established that they have a finer Hausdorff strictly $\sigma$-discrete connected topology. Another result is that a finer Tychonoff connected strictly $\sigma$-discrete topology exists for any Tychonoff topology with a countable network. We show that there are Tychonoff connected spaces with countable network which are not continuous images of connected second countable spaces. It is established also that every connected Tychonoff space $\mathcal {X}$ is an open retract of a connected homogeneous Tychonoff space, while it is not always possible to find a finer connected homogeneous topology on $\mathcal {X}$.
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Additional Information
  • Vladimir V. Tkachuk
  • Affiliation: Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, Mexico, D.F.
  • Email: vova@xanum.uam.mx
  • Received by editor(s): November 14, 1996
  • Received by editor(s) in revised form: April 4, 1997
  • Communicated by: Alan Dow
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3437-3446
  • MSC (1991): Primary 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-98-04476-1
  • MathSciNet review: 1459154