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\(M\)-mappings make their images less cellular. (English) Zbl 0840.54002
Summary: We consider \(M\)-mappings which include continuous mappings of spaces onto topological groups and continuous mappings of topological groups elsewhere. It is proved that if a space \(X\) is an image of a product of Lindelöf \(\Sigma\)-spaces under an \(M\)-mapping then every regular uncountable cardinal is a weak precaliber for \(X\), and hence \(X\) has the Souslin property. An image \(X\) of a Lindelöf space under an \(M\)-mapping satisfies \(\text{cel}_\omega X\leq 2^\omega\). Every \(M\)-mapping takes a \(\Sigma (\aleph_0)\)-space to an \(\aleph_0\)-cellular space. In each of these results, the cellularity of the domain of an \(M\)-mapping can be arbitrarily large.

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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