Difference between revisions of "Task:Characteristic property of the coproduct topology"
From Maths
(Created page with "{{Stub page|grade=A|msg=Demote once a task template is in place which categorises tasks by type or whether or not they've been completed}} ==Statement== Suppose {{MSeq|(X_\alp...") |
(No difference)
|
Latest revision as of 04:38, 7 August 2016
Stub grade: A
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Demote once a task template is in place which categorises tasks by type or whether or not they've been completed
Statement
Suppose [ilmath] ({ (X_\alpha,\mathcal{J}_\alpha) })_{ \alpha = I }^{ \infty } [/ilmath] is an arbitrary collection of non-empty topological spaces, and [ilmath](Y,\mathcal{ K })[/ilmath] is another topological space. Suppose [ilmath]f:\coprod_{\alpha\in I}X_\alpha\rightarrow Y[/ilmath] is a map, then[1]:
- [ilmath]f:\coprod_{\alpha\in I}X_\alpha\rightarrow Y[/ilmath] is continuous if and only if for all [ilmath]\alpha\in I[/ilmath], [ilmath]f\vert_{X_\alpha}:X_\alpha\rightarrow Y [/ilmath] is continuous.
Proof
(Unknown grade)
This page requires one or more proofs to be filled in, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).
References
