On an algebraic version of Tamano’s theorem

Raushan Z. Buzyakova


Let X be a non-paracompact subspace of a linearly ordered topological space. We prove, in particular, that if a Hausdorff topological group G contains closed copies of X and a Hausdorff compactification bX of X then G is not normal. The theorem also holds in the class of monotonically normal spaces.


Topological group; Hausdorff compactification; Normal space; Stationary set

Full Text:



Z. Balogh and M. E. Rudin, Monotone normality, Topology Appl. 47 (1992), no. 2, 115-127. https://doi.org/10.1016/0166-8641(92)90066-9

R. Z. Buzyakova, Ordinals in topological groups, Fund. Math. 196 (2007), no. 2, 127-138. https://doi.org/10.4064/fm196-2-3

D. J. Lutzer, Ordered topological spaces, Surveys in general topology, pp. 247-295, Academic Press, New York-London-Toronto, Ont., 1980. https://doi.org/10.1016/B978-0-12-584960-9.50014-6

O. V. Sipacheva, The topology of free topological group, Fundam. Prikl. Mat. 9 (2003), no. 2, 99-204

English translation in J. Math. Sci. (N. Y.) 131 (2005), no. 4, 5765-5838. https://doi.org/10.1007/s10958-005-0445-z

H. Tamano, On paracompactness, Pacific J. Math. 10 (1960) 1043-1047. http://dx.doi.org/10.2140/pjm.1960.10.1043 https://doi.org/10.2140/pjm.1960.10.1043

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. An algebraic version of Tamano's theorem for countably compact spaces
Raushan Z. Buzyakova
Topology and its Applications  vol: 157  issue: 14  first page: 2289  year: 2010  
doi: 10.1016/j.topol.2010.06.008

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt