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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2007 | 196 | 2 | 127-138

## Ordinals in topological groups

EN

### Abstrakty

EN
We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following statements: (1) If τ and τ + 1 embed closedly in G then τ × (τ + 1) embeds closedly in G; (2) If τ embeds in G, G is Abelian, and the order of every non-neutral element of G is greater than $2^{N} - 1$ then $∏_{i∈N}τ$ embeds in G; (3) The previous statement holds if τ is replaced by τ + 1; (4) If G is Abelian, algebraically generated by τ + 1 ⊂ G, and the order of every element does not exceed $2^{N} - 1$ then $∏_{i∈N}(τ+1)$ is not embeddable in G.

127-138

wydano
2007

### Twórcy

autor
• Mathematics Department, UNCG, Greensboro, NC 27402, U.S.A.