Left and Right Component of the Complement of a Special Closed Curve

The articles [23], [26], [7], [25], [11], [2], [21], [18], [27], [6], [5], [3], [24], [12], [1], [13], [20], [28], [19], [4], [9], [10], [14], [15], [16], [8], [22], and [17] provide the notation and terminology for this paper. For simplicity we adopt the following rules: f will denote a non constant standard special circular sequence, i, j, k will denote natural numbers, p, q will denote points of E2 T, and G will denote a Go-board. The following propositions are true: (1) i−′ i = 0. (2) i−′ j ≤ i. (3) Let G1 be a non empty topological space and let A1, A2, B be subsets of the carrier of G1. Suppose A1 is a component of B and A2 is a component of B. Then A1 = A2 or A1 misses A2. (4) Let G1 be a non empty topological space, and let A, B be non empty subsets of the carrier of G1, and let A3 be a subset of the carrier of G1 B.If A = A3, then G1 A = G1 B A3. (5) Let G1 be a non empty topological space and let A, B be non empty subsets of the carrier of G1. Suppose A ⊆ B and A is connected. Then there exists a subset C of the carrier of G1 such that C is a component of B and A ⊆ C. (6) Let G1 be a non empty topological space and let A, B, C, D be subsets of the carrier of G1. Suppose B is connected and C is a component of D and A ⊆ C and A meets B and B ⊆ D. Then B ⊆ C.