# Tagged Questions

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### Homeomorphism form $(-1,1)$ to $\mathbb{R}$

I want to show that every open intervall $(a,b)$ is homeomorph to $\mathbb{R}$. On $(a,b)$ I chose the relative topology $\mathcal{T}_{(a,b)}$ and on $\mathbb{R}$ the trivial topology $\mathcal{T}$ ...
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### Morphisms between quasiprojective varieties preserve irreducibility

Let $X,Y$ be two quasiprojective varieties and $\phi \colon X \to Y$ a surjective morphism. Let $Z \subset Y$ a closed set such that $\phi^{-1}(Z)$ is irreducible. Prove that $Z$ is irreducible. ...
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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 ...
Assume we are given a space $A$ with a metric $d$. Assume $A = A_1 \times A_2 \times A_3 \cdots$, ie. $A$ is a Cartesian product of spaces $A_i$, where $i \in I$. $I$ is countable or countably ...
Possible Duplicate: Is there “essentially only 1” Jordan arc in the plane? Let $\gamma : [0,1] \to \mathbb{R}^2$ be a simple curve with $\gamma(0)=(0,0)$ and $\gamma(1) =(1,0)$. Clearly, ...