Representation Space with Confluent Mappings

Given a subclass P of the set N of all non-degenerate continua we say X ∈ Cl _Ƒ ( P ) if for every ε > 0 there are a continuum Y ∈ P and a confluent ε-map ƒ : X → Y. This closure operator Cl _Ƒ gives a topology τ _Ƒ on the space N , see [1]. In this article we continue investigation of the topological space ( N ,τ _Ƒ ), 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.