Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Metrizability of sequential topological groups with point-countable $k$-networks

Author(s): Alexander Shibakov
Journal: Proc. Amer. Math. Soc. 126 (1998), 943-947.
MSC (1991): Primary 54H11; Secondary 54D55, 54A20, 54E35
MathSciNet review: 1443165
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We prove that a Hausdorff sequential topological group with a point-countable $k$-network is metrizable iff its sequential order is less than $\omega _{1}$. In the non Hausdorff case metrizability may be replaced by $\sigma $-locally finite base.

References:

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

[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).

[S]
A. Shibakov, Sequential group topology on rationals with intermediate sequential order, Proc. Amer. Math. Soc. 124 (1996), 2599-2607. MR 96j:54032

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

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54H11, 54D55, 54A20, 54E35

Retrieve articles in all Journals with MSC (1991): 54H11, 54D55, 54A20, 54E35

Additional Information:

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

DOI: 10.1090/S0002-9939-98-04139-2
PII: S 0002-9939(98)04139-2
Keywords: Topological group, sequential space, sequential order, Fr\'{e}chet space, $k$-network
Received by editor(s): May 10, 1995
Received by editor(s) in revised form: September 15, 1996
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1998, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia