T_A (x)

For each point x of a continuum X with an arc-structure A we define (see [42, I.3, p. 550]) $T_A (x) = \{y \in X:$ each convex subcontinuum of X with y in its interior contains $\; x\}$. Since T_A (x) is always closed, we have $T_A: X \to 2^X$.