منابع مشابه
Open Mapping Theorem
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, ...
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This note is devoted to two classical theorems: the open mapping theorem for analytic functions (OMT) and the fundamental theorem of algebra (FTA). We present a new proof of the first theorem, and then derive the second one by a simple topological argument. The proof is elementary in nature and does not use any kind of integration (neither complex nor real). In addition, it is also independent ...
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The purpose of this paper is to provide a modified open mapping theorem, which also applies to maps which are not open, but whose intersection with a convex cone is relatively open. We give a constructive proof, which for the special maps considered here may be seen as an alternative to the indirect proof of Frankowska’s more general open mapping principle. Open mapping theorems are of utmost i...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1962
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1962.12.253