All Questions
Tagged with second-countable product-space
3 questions
1
vote
2
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818
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Uncountable product of second countable spaces
Let $(X_i, \mathcal{T}_i)_{i \in I}$ be a family non indiscrete
topological spaces and equip the product with the product topology
$\mathcal{T}$. If $\prod X_i$ is second countable, prove that $|I|...
user370967
16
votes
1
answer
282
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Constraining a dense sequence on a product space, one factor at a time
Slogan: Given a sequence on $X\times Y$, can we choose subsequences to fix the limit in $X$ while leaving the behavior on $Y$ free?
Details: Suppose $X$ and $Y$ are topological spaces and $(x_n,y_n)...
- 27.3k
11
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2
answers
2k
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Compact topological space not having Countable Basis?
Does there exist a compact topological space not having countable basis?
I have constructed a product space from uncountably many unit intervals $[0,1]$, endowed with the product topology. Tychonoff'...
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