Bukatin, Michael, Kopperman, Ralph and Matthews, S. G.. (2009) Partial metric spaces. American Mathematical Monthly, Vol.116 (No.8). pp. 708-718. ISSN 0002-9890

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Abstract

When mathematics is processed on a computer, objects are known only to the extent to which their values are computed; the metric space axiom that says d(x,x)=0 for each point x then becomes the unrealistic assumption that we always know the eventual value of x exactly. The theory of partial metric spacesgeneralizes that of metric spaces by dropping that axiom to allow structures that simultaneously model mathematics and its computer representation. In them, d(x,x)=0 for the ideal, completely known points; d(x,x)not=0 for their partially computed approximations. We discuss how familiar metric and topological reasoning is refined to work in the general setting of convergence and continuity which can now be represented on computers.

Item Type:	Journal Article
Alternative Title:	Michael Bukatin, Ralph Kopperman, Steve Matthews, and Homeira Pajoohesh
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	American Mathematical Monthly
Publisher:	Mathematical Association of America
ISSN:	0002-9890
Date:	October 2009
Volume:	Vol.116
Number:	No.8
Page Range:	pp. 708-718
Identification Number:	10.4169/193009709X460831
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/42371

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