Difference between revisions of "Sierpinski metric"
From Encyclopedia of Mathematics
(Created page with "{{TEX|done}}{{MSC|54E35}} A metric on a countably infinite set $X = \{x_1,x_2,\ldots\}$. For $i \ne j$ define $d(x_i,x_j) = 1 + 1/(i+j)$, and $d(x_i,x_i) = 0$. The Sier...") |
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| − | * Steen, Lynn Arthur; Seebach, J.Arthur jun. ''Counterexamples in topology'' (2nd ed.) Springer (1978) ISBN 0-387-90312-7 {{ZBL|0386.54001}} | + | * Steen, Lynn Arthur; Seebach, J.Arthur jun. ''Counterexamples in topology'' (2nd ed.) Springer (1978) {{ISBN|0-387-90312-7}} {{ZBL|0386.54001}} |
Latest revision as of 19:07, 14 November 2023
2020 Mathematics Subject Classification: Primary: 54E35 [MSN][ZBL]
A metric on a countably infinite set $X = \{x_1,x_2,\ldots\}$. For $i \ne j$ define $d(x_i,x_j) = 1 + 1/(i+j)$, and $d(x_i,x_i) = 0$. The Sierpinski metric is complete, since every Cauchy sequence is ultimately constant. The induced topology is the discrete topology.
References
- Steen, Lynn Arthur; Seebach, J.Arthur jun. Counterexamples in topology (2nd ed.) Springer (1978) ISBN 0-387-90312-7 Zbl 0386.54001
How to Cite This Entry:
Sierpinski metric. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sierpinski_metric&oldid=54460
Sierpinski metric. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sierpinski_metric&oldid=54460