The product topology is the weak topology for which projection are
Topology>Topological Structures> MathWorld Contributors>Barile> Product TopologyThe topology on the Cartesian product This definition extends in a natural way to the Cartesian product of any finite number where In the definition of product topology of The product topology is also called Tychonoff topology, but this should not cause any confusion with the notion of Tychonoff space, which has a completely different meaning. SEE ALSO: Cantor's Discontinuum, Cartesian Product, Cube, Hilbert Cube, Productive Property, Product Metric, Product Space, Tychonoff Plank, Tychonoff Theorem
This entry contributed by Margherita Barile Cullen, H.F. Introduction to General Topology. Boston, MA: Heath, pp.65-91, 1968. Joshi, K.D. "Product Topology." §8.2 in Introduction to General Topology. New Delhi, India: Wiley, pp.196-203, 1983. McCarty, G. "Tychonoff for Two." In Topology, an Introduction with Application to Topological Groups. New York: McGraw-Hill, pp.154-157, 1967. Willard, S. "Product Spaces, Weak Topologies." §8 in General Topology. Reading, MA: Addison-Wesley, pp.52-59, 1970. Referenced on Wolfram|Alpha: Product TopologyCITE THIS AS:Barile, Margherita. "Product Topology." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ProductTopology.html |