A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

Z. Yang

A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

Source

Fundamenta Informaticae > 2008 > Vol. 88, nr 1-2 > 207-223

Abstract

This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.

Identifiers

journal ISSN :	0169-2968
journal e-ISSN :	1875-8681

Authors

Yang, Z.

Department of Mathematics University of the Incarnate Word 4301 Broadway, San Antonio, TX 78209, USA

Keywords

proximity spaces

Additional information

Publication languages: English

Data set: BazTech

Publisher

IOS Press

Fields of science

No field of science has been suggested yet.

Bibliography

[1] Adàmek, J., Herrlich, H., Strecker, G. E.: Abstract and Concrete Categories, The Joy of Cats, John Wiley and Sons, New Work, 1990.
[2] Chaudhuri, B.: A new definition of neighborhood of a point in multi-dimensional space, Pattern Recognition Letters, (17), 1996, 11-17.
[3] Čech, E.: Topological Spaces, Interscience,Wiley, New York, 1966.

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Abstract

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Yang, Z.

Keywords

Additional information

Publisher

Fields of science

Fields of science

Bibliography

[1] Adàmek, J., Herrlich, H., Strecker, G. E.: Abstract and Concrete Categories, The Joy of Cats, John Wiley and Sons, New Work, 1990.

[2] Chaudhuri, B.: A new definition of neighborhood of a point in multi-dimensional space, Pattern Recognition Letters, (17), 1996, 11-17.

[3] Čech, E.: Topological Spaces, Interscience,Wiley, New York, 1966.

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A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces