Original scientific paper

https://doi.org/10.3336/gm.52.1.14

Approximate maps characterizing injectivity and surjectivity of maps

Takahisa Miyata ; Department of Mathematics and Informatics, Graduate School of Human Development and Environment, Kobe University, Kobe, 657-8501, Japan

Abstract

In the theory of inverse systems, in order to study the properties of a space X or a map f: X → Y between spaces, one expands X to an inverse system X or expands f to a map f: X → Y between the inverse systems, and then work on X or f. In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f: X → Y between compact metric spaces is injective (resp., surjective) if and only if any approximate map f:

Keywords

Injective map; surjective map; epimorphism; monomorphism, approximate map; shape

Hrčak ID:

183132

URI

https://hrcak.srce.hr/183132

Publication date:

21.6.2017.

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