Kuratowski - Zorn Lemma

Wojciech A. Trybulec

Warsaw University

Grzegorz Bancerek

Warsaw University, Bialystok

Summary.

The goal of this article is to prove Kuratowski - Zorn lemma. We prove it in a number of forms (theorems and schemes). We introduce the following notions: a relation is a quasi (or partial, or linear) order, a relation quasi (or partially, or linearly) orders a set, minimal and maximal element in a relation, inferior and superior element of a relation, a set has lower (or upper) Zorn property w.r.t. a relation. We prove basic theorems concerning those notions and theorems that relate them to the notions introduced in [8]. At the end of the article we prove some theorems that belong rather to [10], [12] or [2].

Supported by RPBP.III-24.C1.

MML Identifier: ORDERS_2

Contents (PDF format)

Bibliography

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