Representation space with confluent mappings

Given a subclass P of the set N of all non-degenerate continua we say X∈ClF(P) if for every ε>0 there are a continuum Y∈P and a confluent ε-map f:X→Y. This closure operator ClF gives a topology τF on the space N, see [1]. In this article we continue investigation of the topological space (N,τF), we establish interiors and closures of some natural classes of continua, we recall related results and pose several open problems. This gives us a new point of view on topological properties of some classes of continua and on confluent mappings.