Pseudometric space (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pseudometric space" in English language version.

refsWebsite

Global rank English rank

1planetmath.org

low place

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archive.today

Cain, George (Summer 2000). "Chapter 7: Complete pseudometric spaces" (PDF). Archived (PDF) from the original on 7 October 2020. Retrieved 7 October 2020.

gatech.edu

people.math.gatech.edu

Cain, George (Summer 2000). "Chapter 7: Complete pseudometric spaces" (PDF). Archived (PDF) from the original on 7 October 2020. Retrieved 7 October 2020.

planetmath.org

"Pseudometric topology". PlanetMath.

springer.com

Howes, Norman R. (1995). Modern Analysis and Topology. New York, NY: Springer. p. 27. ISBN 0-387-97986-7. Retrieved 10 September 2012. Let $(X,d)$ be a pseudo-metric space and define an equivalence relation $\sim$ in $X$ by $x\sim y$ if $d(x,y)=0$ . Let $Y$ be the quotient space $X/\sim$ and $p:X\to Y$ the canonical projection that maps each point of $X$ onto the equivalence class that contains it. Define the metric $\rho$ in $Y$ by $\rho (a,b)=d(p^{-1}(a),p^{-1}(b))$ for each pair $a,b\in Y$ . It is easily shown that $\rho$ is indeed a metric and $\rho$ defines the quotient topology on $Y$ .