Displaying similar documents to “Concerning dense metric subspaces of certain non-metric spaces”

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M. Jelić (1990)

Matematički Vesnik

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Cardinality of the sets of all bijections, injections and surjections

Marcin Zieliński (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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The results of Zarzycki for the cardinality of the sets of all bijections, surjections, and injections are generalized to the case when the domains and codomains are infinite and different. The elementary proofs the cardinality of the sets of bijections and surjections are given within the framework of the Zermelo-Fraenkel set theory with the axiom of choice. The case of the set of all injections is considered in detail and more explicit an expression is obtained when the Generalized...