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Results tagged with examples
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user 3634
For questions requesting examples of a certain structure or phenomenon
12
votes
Counterexamples in algebraic topology?
There are plenty of examples, generally related to localization.
Probably a good start:
Hilton, P.
Non-cancellation phenomena in topology. Topics in topology (Proc. …
5
votes
Non-homogeneous space $X$ such that $X\cong X\setminus \{x\}$ for all $x\in X$
Take the disjoint union of any two nonhomeomorphic spaces with that property as long as they are perfect, e.g., $\mathbb{Q}\coprod(\mathbb{R}-\mathbb{Q})$.
- 12.5k
5
votes
What are your favorite concrete examples of limits or colimits that you would compute during...
Group actions! Treat $G$ as a category $\mathcal{G}$. Then a $G$-action is a functor $\mathcal{G}\to \mathcal{C}$. Its colimit is the orbit space and its limit is the fixed points.
4
votes
Examples where it's useful to know that a mathematical object belongs to some family of objects
I've written a paper (or two) about collection $\mathcal{R}$ of all pointed topological spaces $Y$ satisfying the
property $\mathrm{map}_*(X,Y) \sim *$ (for fixed $X$). The interesting fact is that
…