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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.

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