Retodic space

In this paper, we introduced the concept of retodic spaces and we investigate its relations with resolvable spaces. ∋For a cardinal alpha, we say that a T_1-space Y is a alpha-retodic space if Y is partitioned by a family {D_ξ}_{ξ alpha} of dense subsets such that the complement of every D_ξ is totally disconnected. It is shown that A locally connected space X is alpha-resolvable if for every connected open subset U⊆X, there exists a alpha-retodic space Y_U and a non-constant continuous function f: U→ Y_U .