A theorem of C. Ryll-Nardzewski and metrizable l.c.a. groups
L. Thomas Ramsey
Proc. Amer. Math. Soc. 78 (1980), 221-224
Primary 43A46; Secondary 03E50
Full-text PDF Free Access
Similar Articles |
Abstract: denotes a metrizable locally compact abelian group and its Bohr compactification. Let be a cluster point of some subset E of in the topology of . Then there are two disjoint subsets of E which also cluster at in the Bohr group topology. The proof is elementary and provides a new proof of the theorem of C. Ryll-Nardzewski on cluster points of I-sets in R. Given the continuum hypothesis, either theorem characterizes metrizability in locally compact abelian groups. One of these characterizations is shown to be equivalent to the continuum hypothesis.
Rudin, Fourier analysis on groups, Interscience Tracts in Pure
and Applied Mathematics, No. 12, Interscience Publishers (a division of
John Wiley and Sons), New York-London, 1962. MR 0152834
Ryll-Nardzewski, Concerning almost periodic extensions of
functions, Colloq. Math. 12 (1964), 235–237. MR 0173129
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic anaylsis, Academic Press, New York, 1963.
- Walter Rudin, Fourier analysis on groups, Wiley, New York, 1969. MR 0152834 (27:2808)
- C. Ryll-Nardzewski, Concerning almost periodic extensions of functions, Colloq. Math. 12 (1964), 235-237. MR 0173129 (30:3344)
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic anaylsis, Academic Press, New York, 1963.
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
© Copyright 1980 American Mathematical Society