Viewing topic: Box Topology

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Box Topology

  • Definition: Let {X_a} be a family of indexed topological spaces. Let Y denote the generalized Cartesian product of the sets X_a. Let B denote the set of all products of open sets of the corresponding spaces. Now we can construct the box product (Y, S) , where S, referred to as the box topology, is the topology generated by the base B. When A is a finite set, the box topology coincides with the product topology.

    Source: http://planetmath.org/encyclopedia/BoxProduct.html

  • Example: For technical notation, please see the source website.

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