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WannaBe22
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[Topology] Product Spaces :(
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.
I've no idea how to start thinking of these questions...
I'll be delighted to receive some guidance
Thanks in advance
Homework Statement
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.
Homework Equations
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