Fan Homeomorphisms in the Plane
نویسنده
چکیده
In this paper x, a denote real numbers and p, q denote points of E2 T. The following propositions are true: (1) If |x| < a, then −a < x and x < a. (2) If a 0 and (x− a) · (x + a) < 0, then −a < x and x < a. (3) For every real number s1 such that −1 < s1 and s1 < 1 holds 1 + s1 > 0 and 1− s1 > 0. (4) For every real number a such that a2 ¬ 1 holds −1 ¬ a and a ¬ 1. (5) For every real number a such that a2 < 1 holds −1 < a and a < 1. (6) Let X be a non empty topological structure, g be a map from X into R1, B be a subset of X, and a be a real number. If g is continuous and B = {p; p ranges over points of X: πpg > a}, then B is open. (7) Let X be a non empty topological structure, g be a map from X into R1, B be a subset of X, and a be a real number. If g is continuous and B = {p; p ranges over points of X: πpg < a}, then B is open.
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