Computability of Generalized Graphs

We investigate conditions under which a semicomputable set is computable. In particular, we study topological pairs (A,B) which have a computable type, which means that in any computable topological space, a semicomputable set S is computable if there exists a semicomputable set T such that (S,T) is homeomorphic to (A,B). It is known that (G,E) has a computable type if G is a topological graph and E is the set of all its endpoints. Furthermore, the same holds if G is a so-called chainable graph. We generalize the notion of a chainable graph and prove that the same result holds for a larger class of spaces.