# Tagged Questions

For question about morphism between groups, ring, topological spaces, vector space, categories, etcs... Please also use the correspondent tags (e.g. (group-theory), (ring-theory)) in order to precise the involved structure.

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### Riesz homomorphism (Banach-Stone theorem)

Let $X,Y$ be compact Haussdorff spaces, and consider $$J:C(X)\to C(Y)$$ a bounded linear bijection such that $J(f\cdot g) = J(f)J(g)$. I know that if $T:C(X)\to C(Y)$ is a linear bijection, being ...
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### if a map is bijective, then it has inverse. is the inverse also bijective?

I asked this question because I want to know if given two groups that are isomorphic will always have the same order or not.
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### Hypergraph notation and hypergraph morphisms

There are two parts to my question. The first part is about notation for hypergraphs. The sconed is about the notion of morphisms for hypergraphs. For the notation part, the context is that I make ...
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### Path Connectedness and continuous bijections

Mathoverflow. Are there any two topological spaces $X$ and $Y$ such that they are path connected and such that there exist continuous bijections $X\rightarrow Y$ and $Y\rightarrow X$, but and yet ...
Let $(G,\cdot), (H,*)$ Groups and $f: G\rightarrow H$ an Epimorphism. Show that: If G is an abelian group, then H is also an abelian group. Is the reversal of this proposition also true? My idea: ...