AXIOM OF CHOICE AND ZORN'S LEMMA IN CANTOR CATEGORIES
نویسندگان
چکیده
منابع مشابه
The Axiom of Choice and Zorn’s Lemma
function on A is thus a choice of an element of the variable set A at each stage; in other words, a choice function on A is just a variable (or global) element of A . The axiom of choice (AC) asserts that if each member of a family A is nonempty, then there is a choice function on A . Metaphorically, then, the axiom of choice asserts that any family of sets with an element at each stage has a v...
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§9.1 The Axiom of Choice We come now to the most important part of set theory for other branches of mathematics. Although infinite set theory is technically the foundation for all mathematics, in practice it is perfectly valid for a mathematician to ignore it – with two exceptions. Of course most of the basic set constructions as outlined in chapter 2 (unions, intersections, cartesian products,...
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متن کاملThe Axiom of Choice
We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
متن کاملThe Axiom of Choice
We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
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ژورنال
عنوان ژورنال: Bulletin of informatics and cybernetics
سال: 2017
ISSN: 0286-522X
DOI: 10.5109/2232319