Some Proximate Concepts in Topology.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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Some of the basic parts of the theory of absolute retracts are developed in a proximate form in which continuous functions are replaced by nearly continous functions, fixed points by nearly fixed points, etc. These notions seem natural in connection with the mathematical modeling of physical problems, where there may be strong empirical evidence for the near continuity of a map even though its full continuity cannot be tested experimentally. And in many applied situations, the conclusions as well as the hypotheses are naturally of a proximate nature. The principal purpose of the paper is to point out the possible advantages and relative lack of pain in studying nearly continuous maps more systematically than they have been studied in the past. Author
- Theoretical Mathematics