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Journal Articles Topology and its Applications Year : 1993

The Ellis theorem and continuity in groups

Ahmed Bouziad
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Abstract

Various theorems which are valid in the presence of metrizability or compactness can be generalized to the class of p-spaces. In this paper, we show that this is the case for the classical theorem of Ellis on joint continuity. As an application, we show that the multiplication is continuous in a semitopological Baire group, which is a paracompact p-space; and that, a Cech-complete semitopological group is a topological group if and only if this group is paracompact. A topological game condition, which insures that a group with a continuous multiplication has a continuous inversion is given.
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hal-00373431 , version 1 (05-04-2009)

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  • HAL Id : hal-00373431 , version 1

Cite

Ahmed Bouziad. The Ellis theorem and continuity in groups. Topology and its Applications, 1993, 50 (Issue 1), pp.73-80. ⟨hal-00373431⟩
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