# Analogies to the Cantor-Schro¨der-Bernstein theorem

- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Lynne Marie Davis (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Robert Bernhardt

**Abstract:** Let A and B be sets, let f be a one-to-one function from A into B, and let g be a one-to-one function from B into A. The Cantor-Schroder-Bernstein Theorem states that there exists a one-to-one function h from A onto B. This theorem is well known, and has long been important in set theory. We present a proof of this theorem in Chapter I. In mathematics, the concept of an isomorphism is of great importance. The word "isomorphism" means different things in different contexts. Perhaps one can intuitively define this term in general as follows: if X is a certain type of mathematical structure, consisting of a set and possibly one or more binary operations,, relations, orders, or topologies; and if Y is a mathematical structure of the same type (meaning Y is a set with the same kinds of binary operations, relations, orders, or topologies); then X is isomorphic to Y provided there is a one-to-one function from X onto Y which preserves these binary operations, relations, orders, or topologies.

Analogies to the Cantor-Schro¨der-Bernstein theorem

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Created on 1/1/1973

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## Additional Information

- Publication
- Thesis
- Language: English
- Date: 1973
- Subjects
- Set theory
- Vector spaces
- Finite groups
- Abelian groups
- Topological spaces

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