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On classes of maps with the extension property to the bicompletion in quasi-pseudo metric spaces

Extensions of CS-regular maps from a dense subset of a metric space to the whole space are discussed in the literature. It is the purpose of this paper to present results on extensions of these maps to the bicompletion in separated quasi-pseudo metric spaces, and in addition we discuss extensions of maps that preserve some special property. Finally, an analogue of the Tietze extension theorem will be discussed in this context.