(adsbygoogle = window.adsbygoogle || []).push({}); [Topology] Product Spaces :(

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

1. Show that in the product space [tex]N^N[/tex] where the topology on N is discrete, the set of near-constant functions is dense (near constant function is a function that becomes constant from a specific index..)...

2. Prove that in [tex]R^I[/tex] the set of monotonic increasing functions is not open.

2. Relevant equations

3. The attempt at a solution

I've no idea how to start thinking of these questions....

I'll be delighted to receive some guidance

Thanks in advance

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# Homework Help: [Topology] Product Spaces

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