Homeomorphisms of Jordan Curves
نویسندگان
چکیده
The notation and terminology used in this paper are introduced in the following articles: [20], [21], [1], [3], [22], [4], [5], [19], [10], [18], [7], [17], [11], [2], [8], [9], [16], [13], [14], [15], [6], [23], and [12]. In this paper p1, p2 are points of E 2 T, C is a simple closed curve, and P is a subset of E T. Let n be a natural number, let A be a subset of En T, and let a, b be points of En T. We say that a and b realize maximal distance in A if and only if: (Def. 1) a ∈ A and b ∈ A and for all points x, y of En T such that x ∈ A and y ∈ A holds ρ(a, b) ≥ ρ(x, y). Next we state the proposition (1) There exist p1, p2 such that p1 and p2 realize maximal distance in C. Let M be a non empty metric structure and let f be a map from Mtop into Mtop. We say that f is isometric if and only if: (Def. 2) There exists an isometric map g from M into M such that g = f. Let M be a non empty metric structure. Note that there exists a map from Mtop into Mtop which is isometric. Let M be a non empty metric space. Observe that every map from Mtop into Mtop which is isometric is also continuous.
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