Product metrics and boundedness


  • Gerald Beer California State University Los Angeles



Product metric, Metric of uniform convergence, Bornology, Convergence to infinity


This paper looks at some possible ways of equipping a countable product of unbounded metric spaces with a metric that acknowledges the boundedness characteristics of the factors.


Download data is not yet available.

Author Biography

Gerald Beer, California State University Los Angeles

Department of Mathematics


G. Beer, On metric boundedness structures, Set-Valued Anal. 7 (1999), 195-208.

G. Beer, On convergence to infinity, Monat. Math. 129 (2000), 267-280.

G. Beer, Metric bornologies and Kuratowski-Painlev´e convergence to the empty set, J. Convex Anal. 8 (2001), 279-289.

J. Borwein, M. Fabian, and J. Vanderwerff, Locally Lipsschitz functions and bornological derivatives, CECM Report no. 93:012.

A. Caterino and S. Guazzone, Extensions of unbounded topological spaces, Rend. Sem. Mat. Univ. Padova 100 (1998), 123-135.

A. Caterino, T. Panduri, and M. Vipera, Boundedness, one-pont extensions, and B-extensions, Math. Slovaca 58, no. 1 (2008), 101–114.

J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.

R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977.

H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland, Amsterdam, 1977.

S.-T. Hu, Boundedness in a topological space, J. Math Pures Appl. 228 (1949), 287-320.

S.-T. Hu, Introduction to general topology, Holden-Day, San Francisco, 1966.

A. Lechicki, S. Levi, and A. Spakowski, Bornological convergences, J. Math. Anal. Appl. 297 (2004), 751-770.

A. Taylor and D. Lay, Introduction to functional analysis, Wiley, New York, 1980.

H. Vaughan, On locally compact metrizable spaces, Bull. Amer. Math. Soc. 43 (1937),532-535.


How to Cite

G. Beer, “Product metrics and boundedness”, Appl. Gen. Topol., vol. 9, no. 1, pp. 133–142, Apr. 2008.