Some categorical aspects of the inverse limits in ditopological context

摘要

This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if PDitop , whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category Inv ifPDitop consisting of the inverse systems constructed by the objects and morphisms of if PDitop , besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if PDitop and the ditopological infinite products are characterized by the finite products via inverse limits.