neat

A dendroid X is said to be neat provided that each one of its subdendroids has no improper shore point (see [71, p. 939]). Let $\mathfrak M$ be a class of mappings. A class $\mathfrak M$ of mappings is said to be neat provided that if all homeomorphisms are in $\mathfrak M$ and the composition of any two mappings in $\mathfrak M$ is also in $\mathfrak M$.