Every uncountable abelian group admits a nonnormal group topology

Author:
F. Javier Trigos-Arrieta

Journal:
Proc. Amer. Math. Soc. **122** (1994), 907-909

MSC:
Primary 22B05; Secondary 54A10, 54A25, 54H11

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209100-7

MathSciNet review:
1209100

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Abstract | References | Similar Articles | Additional Information

Abstract: If **G** is a locally compact Abelian group, let denote the underlying group of **G** equipped with the weakest topology that makes all the continuous characters of **G** continuous. Thus defined, is a totally bounded topological group. We prove:

**Theorem**. *is normal if and only if* **G** *is* -*compact*.

When **G** is discrete, this theorem answers in the negative a question posed in 1990 by E. van Douwen, and it partially solves a problem posed in 1945 by A. Markov.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209100-7

Keywords:
Normal space,
independent set,
Bohr compactification,
totally bounded topology

Article copyright:
© Copyright 1994
American Mathematical Society