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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Sequential group topology on rationals with intermediate sequential order

Author(s): Alexander Shibakov
Journal: Proc. Amer. Math. Soc. 124 (1996), 2599-2607.
MSC (1991): Primary 54D55, 54A20
MathSciNet review: 1353400
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Abstract | References | Similar articles | Additional information

Abstract: Using CH we construct a countable sequential topological group whose sequential order is between $2$ and $\omega $ giving a consistent negative answer to P. Niykos' question.

References:

[A1]
A. Arkhangel$'$skii, Topological properties in topological groups, XVIII All Union Algebraic Conference, Kishinev, 1985. (Russian)

[DP]
S. Dolecki, R. Peirone, Topological semigroups of every countable sequential order, Recent Developments of General Topology and its Applications, Academie Verlag, 1992, pp. 80--84. MR 94c:54073

[F]
L. Foged, Sequential order of homogeneous and product spaces, Topology Proceedings 6 (1981), 287--298. MR 84e:54023

[GMT]
G. Gruenhage, E. Michael, Y. Tanaka, Spaces determined by point-countable covers, Pacif. J. Math. 113 (1984), 303--332. MR 85m:54018

[M1]
E. Michael, $\aleph _0$-spaces, J. of Math. and Mech. 15 (1966), 983--1002. MR 34:6723

[M2]
E. Michael, A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91--138. MR 46:8156

[N]
P. J. Nyikos, Metrizability and Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), 793--801. MR 82k:54049

[NST1]
T. Nogura, D. Shakhmatov, Y. Tanaka, Metrizability of topological groups having weak topologies with respect to good covers, Topology Appl. 54 (1993), 203--212. MR 95b:54046

[NST2]
T. Nogura, D. Shakhmatov, Y. Tanaka, $\alpha _4$-property versus $A$-property in topological spaces and groups (to appear).

[P]
R. Peirone, Regular semitopological groups of every countable sequential order, preprint.

[R]
M. Rajagopalan, Sequential order and spaces $S_n$, Proc. Amer. Math. Soc. 54 (1976), 433--438. MR 52:15377

[ZP]
Zelenyuk, Protasov, Topologies on Abelian groups, Math. USSR Izvestia 37 (1991), 445--460. MR 93b:22001

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Additional Information:

Alexander Shibakov
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email: shobaay@mallard.duc.auburn.edu

DOI: 10.1090/S0002-9939-96-03636-2
PII: S 0002-9939(96)03636-2
Keywords: Topological group, sequential space, sequential order, Fr\'{e}chet space
Received by editor(s): February 24, 1995
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1996, American Mathematical Society




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