On an algebraic version of Tamano’s theorem

Raushan Z. Buzyakova

United States

University of North Carolina Greensboro (UNCG)

Mathematics Department

Submitted: 2013-09-30

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Accepted: 2013-09-30

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DOI: https://doi.org/10.4995/agt.2009.1735
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Keywords:

Topological group, Hausdorff compactification, Normal space, Stationary set

Supporting agencies:

This research was not funded

Abstract:

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.
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References:

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

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