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

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