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Retracts of ultrahomogeneous structures in the context of Katětov functors

Mašulović D.

Demonstratio Mathematica

2015

Vol. 48, nr 4

562--577

In this paper, we characterize retracts of a wide class of Fraïssé limits using the tools developed in a recent paper by W. Kubiś and the present author, which we refer to as Katětov functors. This approach enables us to conclude that in many cases, a structure is a retract of a Fraïssé limit if and only if it is algebraically closed in the surrounding category.

A note on absolute approximate retracts

Martin J.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 4

355-359

The notion of an absolute approximate retract for a class Q of topological spaces (or an AAR(Q)-space) generalizes the concept of an absolute retract for the class Q. For many classes Q, it is shown that AAR(Q)-spaces are preserved under retraction mappings and that a fully normal AAR(Q)-space X must be contractible and can be expressed as a product of finite-dimensional compacta if and only if X is homeomorphic to a cube or is a finite-dimensional AR-space.