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Weak continuity properties of topologized groups

J. Cao, R. Drozdowski, Zbigniew Piotrowski (2010)

Czechoslovak Mathematical Journal

We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if ( G , · , τ ) is a regular right (left) semitopological group with dev ( G ) < Nov ( G ) such that all left (right) translations are feebly continuous, then ( G , · , τ ) is a topological group. This extends several results in literature.

Wildness in the product groups

G. Hjorth (2000)

Fundamenta Mathematicae

Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.

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