Abstract
In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.
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Berzig, M., Kedim, I. Eilenberg–Jachymski collections and its first consequences for the fixed point theory. J. Fixed Point Theory Appl. 23, 26 (2021). https://doi.org/10.1007/s11784-021-00854-4
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DOI: https://doi.org/10.1007/s11784-021-00854-4