(adsbygoogle = window.adsbygoogle || []).push({}); Proving a Set is Closed (Topology)

1. The problem statement, all variables and given/known data

Let [itex]Y[/itex] be an ordered set in the order topology with [itex]f,g:X\rightarrow Y[/itex] continuous. Show that the set [itex]A = \{x:f(x)\leq g(x)\}[/itex] is closed in [itex]X[/itex].

2. Relevant equations

3. The attempt at a solution

I cannot for the life of me figure this out. As far as I can tell one either needs to show the set A gathers its limit points or that it is the pre-image (under f or g) of some closed set in Y. We know the order topology is Hausdorff, so that's something. I just don't even know how to get started on this one. Hopefully someone can help, thanks.

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# Homework Help: Proving a Set in the Order Topology is Closed

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