Every locally connected functionally Hausdorff space is c-resolvable

For a cardinal κ  , we say that a T1T1-space Y is a κ-retodic space if Y   is partitioned by a family {Dξ}ξ∈κ{Dξ}ξ∈κ of dense subsets such that the complement of every DξDξ is totally disconnected. It is shown that “A locally connected space X is κ  -resolvable if for every connected open subset U⊆XU⊆X, there exists a κ  -retodic space YUYU and a non-constant continuous function f:U⟶YUf:U⟶YU”. Consequently, every locally connected functionally Hausdorff space is c-resolvable, which is an answer to the question of K. Padmavally about resolvability of locally connected spaces, and also every c  -irresolvable locally connected T1T1 space contains an open connected subset in which all continuous functions on it to any c-retodic space (all real continuous functions on it) are constant.