Properties of Left and Right Components

For simplicity, we adopt the following rules: r denotes a real number, i, j, n denote natural numbers, f denotes a non constant standard special circular sequence, g denotes a clockwise oriented non constant standard special circular sequence, p, q denote points of E T , P , Q, R denote subsets of E T , C denotes a compact non vertical non horizontal subset of E T , and G denotes a Go-board. Next we state several propositions: (1) Let T be a topological space, A be a subset of the carrier of T , and B be a subset of T . If B is a component of A, then B is connected. (2) Let A be a subset of the carrier of E T and B be a subset of E T . If B is inside component of A, then B is connected. (3) Let A be a subset of the carrier of E T and B be a subset of E T . If B is outside component of A, then B is connected. (4) For every subset A of the carrier of E T and for every subset B of E T such that B is a component of A holds A ∩ B = ∅. (5) If P is outside component of Q and R is inside component of Q, then P ∩ R = ∅.