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Extension theorems in axiomatic theory of convexity

Kubiś W.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

89-96

We present a criterion for extending convexity preserving maps of convexity spaces. In a special case of convexity generated by a lattice structure this gives Sikorski's Extension Criterion for extending of maps of lattices. We also consider the class of convexity absolute extensors. It appears that complete Boolean algebras with a natural convexity belong to this class. In particular, we present an analogue of Tietze-Urysohn's Extension Theorem for maps of convexity spaces with values in a complete Boolean algebra.