Open Mapping Theorem
نویسندگان
چکیده
The notation and terminology used here are introduced in the following papers: [13], [14], [3], [9], [2], [7], [1], [4], [5], [10], [6], [12], [11], and [15]. The following proposition is true (1) For all real numbers x, y such that 0 ≤ x < y there exists a real number s0 such that 0 < s0 and x < y 1+s0 < y. The scheme RecExD3 deals with a non empty set A, an element B of A, an element C of A, and a 4-ary predicate P, and states that: There exists a function f from N into A such that f(0) = B and f(1) = C and for every element n of N holds P[n, f(n), f(n + 1), f(n+ 2)] provided the parameters meet the following requirement: • For every element n of N and for all elements x, y of A there exists an element z of A such that P[n, x, y, z]. In the sequel X, Y denote real normed spaces. The following propositions are true: (2) For every point y1 of X and for every real number r holds Ball(y1, r) = y1 +Ball(0X , r). (3) For every real number r and for every real number a such that 0 < a holds Ball(0X , a · r) = a · Ball(0X , r).
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ورودعنوان ژورنال:
- Formalized Mathematics
دوره 16 شماره
صفحات -
تاریخ انتشار 2008