Continuous reducibility: functions versus relations

It is proved that the Tang-Pequignot reducibility (or reducibility by relatively continuous relations) on a  second countable, T₀ space X either coincides with the Wadge reducibility for the given topology, or there is no topology on X that can turn it into Wadge reducibility.

Received 11 July 2018

AMS subject classificastion: Primary 03E15; Secondary 03D55

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