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Neither first countable nor Cech-complete spaces
are maximal Tychonoff connected


Authors: D. B. Shakhmatov, M. G. Tkacenko, V. V. Tkachuk, S. Watson and R. G. Wilson
Journal: Proc. Amer. Math. Soc. 126 (1998), 279-287
MSC (1991): Primary 54H11, 54C10, 22A05, 54D06; Secondary 54D25, 54C25
DOI: https://doi.org/10.1090/S0002-9939-98-04203-8
MathSciNet review: 1443164
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Abstract | References | Similar Articles | Additional Information

Abstract: A connected Tychonoff space $X$ is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on $X$. We show that if $X$ is a connected Tychonoff space and $X\in \{$locally separable spaces, locally \v{C}ech-complete spaces, first countable spaces$\}$, then $X$ is not maximal Tychonoff connected. This result is new even in the cases where $X$ is compact or metrizable.


References [Enhancements On Off] (What's this?)

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Additional Information

D. B. Shakhmatov
Affiliation: Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan
Email: dmitri@dpc.ehime-u.ac.jp

M. G. Tkacenko
Affiliation: Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F.
Email: mich@xanum.uam.mx

V. V. Tkachuk
Affiliation: Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3
Email: vova@xanum.uam.mx

S. Watson
Affiliation: Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3
Email: stephen.watson@mathstat.yorku.ca

R. G. Wilson
Affiliation: Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F.
Email: rgw@xanum.uam.mx

DOI: https://doi.org/10.1090/S0002-9939-98-04203-8
Keywords: Connected space, separable space, \v{C}ech-complete space, first countable space, finer connected topology, maximal connected topology
Received by editor(s): April 8, 1996
Additional Notes: The research of the second, third, fourth, and fifth authors was supported by the Mexican National Council of Science and Technology (CONACYT), Grant no. 4874E-9406.
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1998 American Mathematical Society

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