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10:04 AM
In the meantime there are 3 more questions tagged .
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Q: Does the function $f(x)=x^2$ admit a continuous extension to the Stone-Cech compactification?

MichaelDoes the function $f(x)=x^2$ admit a continuous extension $\widetilde{f}:\beta\mathbb{R}\longrightarrow\mathbb{R}$ to the Stone-Cech compactification? Proof. If $f$ admitted a continuous extension to the Stone-Cech compactification, then the triangle/maps would commute. The triangle being: $f =...

1
Q: What does the 1-point compactification of disjoint open intervals look like?

John SwoonCan someone explain, given a set of disjoint open intervals, does the 1 point compactification look more like: Or Also how do we know that the compactification would necessarily be in a higher dimension?

2
Q: Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff

John Swoonhttps://en.wikipedia.org/wiki/Alexandroff_extension Definition: one point compactification Let $X$ be any topological space, and let $ \infty$ be any object which is not already an element of $X$. Put $ X^{*}=X\cup \{\infty \}$, and topologize $X^* $ by taking as open sets all the o...

 
10:16 AM
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A: Tag management 2016

Martin SleziakThe tag compactification was created a few days ago. This tag has been created and removed before. At the moment there are 4 questions with this tag. Somewhat related tag was discussed here: Would tags such as "ultrafilters" or "Stone-Cech compactification" be too specific? After that discussio...

 

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