Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516663 | Topology and its Applications | 2005 | 13 Pages |
Abstract
Several new facts concerning topologies of paratopological and semitopological groups are established. It is proved that every symmetrizable paratopological group with the Baire property is a topological group. If a paratopological group G is the preimage under a perfect homomorphism of a topological group, then G is also a topological group. If a paratopological group G is a dense Gδ-subset of a regular pseudocompact space X, then G is a topological group. If a paratopological group H is an image of a totally bounded topological group G under a continuous homomorphism, then H is also a topological group. If a first countable semitopological group G is Gδ-dense in some Hausdorff compactification of G, then G is a topological group metrizable by a complete metric. We also establish certain new connections between cardinal invariants in paratopological and semitopological groups. In particular, it is proved that if G is a bisequential paratopological group such that GÃG is Lindelöf, then G has a countable network. Under (CH), we prove that if G is a separable first countable paratopological group such that GÃG is normal, then G has a countable base. This sheds a new light on why the square of the Sorgenfrey line is not normal.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
A.V. Arhangel'skii, E.A. Reznichenko,