The Brouwer Fixed Point Theorem for Intervals1
نویسنده
چکیده
(1) If a≤ c and d ≤ b, then [c,d]⊆ [a,b]. (2) If a≤ c and b≤ d and c≤ b, then [a,b]∪ [c,d] = [a,d]. (3) If a≤ c and b≤ d and c≤ b, then [a,b]∩ [c,d] = [c,b]. (4) For every subset A of R1 such that A = [a,b] holds A is closed. (5) If a≤ b, then [a, b]T is a closed subspace of R1. (6) If a≤ c and d ≤ b and c≤ d, then [c, d]T is a closed subspace of [a, b]T. (7) If a≤ c and b≤ d and c≤ b, then [a, d]T = [a, b]T∪ [c, d]T and [c, b]T = [a, b]T∩ [c, d]T. Let a, b be real numbers. Let us assume that a ≤ b. The functor a[a,b]T yields a point of [a, b]T and is defined as follows:
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