Partial metric spaces
Bukatin, Michael, Kopperman, Ralph and Matthews, S. G.. (2009) Partial metric spaces. American Mathematical Monthly, Vol.116 (No.8). pp. 708-718. ISSN 0002-9890Full text not available from this repository.
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|
|Official Date:||October 2009|
|Page Range:||pp. 708-718|
|Access rights to Published version:||Restricted or Subscription Access|
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