Abstract
The notions of the relative cellularity (≡ relative Souslin number) c( X, Y) and the relative τ-cellularity cel τ ( X, Y) of a subspace X of a topological space Y are introduced. Always c( X)⩾ c( X, Y)⩽cel τ ( X, Y)⩽ cel τ ( X). It is proved that cel τ ( X, G) ⩽exp τ for any τ-Lindelöf subspace X of any Hausdorff topological group G and c( X)⩽cel τ ( X)⩽ exp τ if, in addition, X is a retract of G or even a retract of some G τ-subset of G. These results are deduced form the results concerning spaces with lattices of open mappings on them.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
