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Neither first countable nor Cech-complete spaces are maximal Tychonoff connected
Author(s):
D.
B.
Shakhmatov;
M.
G.
Tkacenko;
V.
V.
Tkachuk;
S.
Watson;
R.
G.
Wilson
Journal:
Proc. Amer. Math. Soc.
126
(1998),
279-287.
MSC (1991):
Primary 54H11, 54C10, 22A05, 54D06;
Secondary 54D25, 54C25
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Abstract:
A connected Tychonoff space  is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on  . We show that if  is a connected Tychonoff space and  locally separable spaces, locally \v{C}ech-complete spaces, first countable spaces , then  is not maximal Tychonoff connected. This result is new even in the cases where  is compact or metrizable.
References:
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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:
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. Michoacán y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México, D.F.
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:
10.1090/S0002-9939-98-04203-8
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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