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Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

Michael M. Zarichnyi — 1991

Commentationes Mathematicae Universitatis Carolinae

We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.

A note on operators extending partial ultrametrics

Edward D. Tymchatyn;  Michael M. Zarichnyi — 2005

Commentationes Mathematicae Universitatis Carolinae

We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.

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