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A countable nondiscrete topological field without nontrivial convergent sequences
Author(s):
Alexander
Shibakov
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3091-3094.
MSC (1991):
Primary 54H13;
Secondary 54A20
Posted:
April 28, 1999
MathSciNet review:
1600137
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Abstract:
A construction of a space in the title is presented, answering a question asked by A. Arkhangel skii and D. Shakhmatov.
References:
- [vD]
- E. van Douwen, The maximal totally bounded topology on
 and the biggest minimal -space for Abelian groups , Topology Appl. 34 (1990), 69-91. - [M]
- E. Michael, Bi-quotient maps and Cartesian products of quotient maps, Ann. Inst. Fourier (Grenoble) 18 (1968), 287-302. MR 39:6277
- [MMO]
- J. Mack, S. Morris, E. Ordman, Free topological groups and the projective dimension of a locally compact abelian group, Proc. Amer. Math. Soc. 40 (1973), 303-308. MR 47:8755
- [S1]
- D. B. Shakhmatov, Condensations of universal topological algebras preserving continuity of operations and decreasing weights, Moscow Univ. Math. Bull. 39 (1984), 42-45. MR 85h:22003
- [S2]
- D. B. Shakhmatov, The structure of topological fields and cardinal invariants, Trans. Moscow Math. Society 50 (1987), 249-259. MR 89c:54076
- [W]
- W. Wies{\l}aw, Topological fields, Marcel Dekker, Inc., New York, 1988. MR 89i:12007
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Additional Information:
Alexander
Shibakov
Affiliation:
Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505
Email:
ashibakov@tntech.edu
DOI:
10.1090/S0002-9939-99-04854-6
PII:
S 0002-9939(99)04854-6
Keywords:
Topological field,
convergent sequence
Received by editor(s):
March 25, 1997
Received by editor(s) in revised form:
December 12, 1997
Posted:
April 28, 1999
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
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