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Spaces of continuous step functions over LOTS

100%

Buzyakova R.

Fundamenta Mathematicae

2006

tom 192

nr 1

25-35

We investigate spaces $C_{p}(·,n)$ over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of $C_{p}(·,n)$ over LOTS. We also characterize countably compact LOTS whose $C_{p}(·,n)$ is linearly Lindelöf for each n. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.

Ordinals in topological groups

100%

Buzyakova R.

Fundamenta Mathematicae

2007

tom 196

nr 2

127-138

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.

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2 Fundamenta Mathematicae

2 Buzyakova R.

1 2007

1 2006

Wyniki wyszukiwania

Spaces of continuous step functions over LOTS

Ordinals in topological groups