Tagged Questions
1
vote
1answer
131 views
Homeomorphism of product of topological spaces
I am stuck on a problem about homeomorphic topological spaces and can't go on...
So the problem is:
If we have that $X_{1} \times X_{2}\simeq Y_{1} \times Y_{2}$ (the product of topological spaces X1 ...
0
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1answer
145 views
Definition of product of uniform spaces
In Wikipedia and PlanetMath product of uniform spaces is defined as the weakest uniformity on the Cartesian product making all the projection maps uniformly continuous.
But Springer's encyclopedia ...
5
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1answer
116 views
Continuous maps from products of topological spaces
Let $X,Y,Z$ be topological spaces. It is well-known that if $F:X\times Y\to Z$ is a continuous map, we can define a map $$\overline{F}:X\to C(Y,Z) \\\overline{F}(x)(y)=F(x,y)$$ where $C(Y,Z)$ is the ...
3
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1answer
161 views
Is $\prod_{\mathbb{R}}\mathbb{R} = \mathbb{R}^\mathbb{R}$?
(If the title is unclear, I'm looking at infinite cartesian product of $\mathbb{R}$ indexed by $\mathbb{R}$.)
I thought that I had reasoned this rather well, as follows:
$\mathbb{R}^\mathbb{R} = ...
