Sequential completeness and spaces with the gliding Humps property.

Dominikus Noll

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S. Franklin (1967)

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∗ Supported by the Serbian Scientific Foundation, grant No 04M01 We consider some relations between p-sequential-like properties and cleavability of topological spaces. Under a special assumption we give an very easy proof of the following result of A.V. Arhangel’skii (the main result in [1]): if a (countably) compact space X is cleavable over the class of sequential spaces, then X is also sequential.

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Roman Frič (1976)

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Roman Frič (1993)

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We investigate free groups over sequential spaces. In particular, we show that the free $k$ -group and the free sequential group over a sequential space with unique limits coincide and, barred the trivial case, their sequential order is $ω_{1}$ .

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