Secondcountability is countable productclosed
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Revision as of 16:52, 21 July 2008 by Vipul (talk  contribs) (New page: {{topospace metaproperty satisfaction}} ==Statement== A product of countably many secondcountable spaces, given the product topology, is also a secondcountable space. ==Relate...)
This article gives the statement, and possibly proof, of a topological space property satisfying a topological space metaproperty
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Property "Page" (as page type) with input value "{{{property}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
Property "Page" (as page type) with input value "{{{metaproperty}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
Statement
A product of countably many secondcountable spaces, given the product topology, is also a secondcountable space.
Related facts
The result is not true if we give the box topology to the product space.
Proof
Given: A countable family of spaces , with each having a countable basis . is the product of the s, given the product topology
To prove: is a secondcountable space