Electronic Version 19 (1994), 321-334

Vladimir V. Tkachuk

We call a space metrizably fibered if it maps continuously and with metrizable fibers onto a metrizable space. Most of our attention is concentrated on the class M of metrizably fibered compact spaces. It is evident that M is a subclass of the class FC of first countable compact spaces. We prove that M is strictly smaller than FC and that M is invariant with respect to open maps while not being invariant under continuous mappings. It is established that if perfectly normal compact space is metrizably fibered, then so are all its continuous images. We also introduce the concept of weakly metrizably fibered space and show that any Eberlein compact space of weight less than or equal to continuum is weakly metrizably fibered, while under the negation of the Souslin hypothesis there exist perfectly normal Corson compact spaces of cardinality \omega₁ which are not weakly metrizably fibered.

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volume 19: table of contents
topology proceedings Electronic Version