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## Spaces with unique endomorphism monoids

If $(X,\tau)$ is a topological space, let $\text{End}(X)$ denote the collection of all continuous maps $f: X\to X$. With composition, this becomes the endomorphism monoid $(\text{End}(X), \circ)$. We say that the space $X$ has a unique endomorphism monoid if $\text{End}(X) \cong \text{End}(Y)$ as monoids, for some space $Y$, then the spaces $X$ and $Y$ are […]

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## Spaces with unique endomorphism monoids

If $(X,\tau)$ is a topological space, let $\text{End}(X)$ denote the collection of all continuous maps $f: X\to X$. With composition, this becomes the endomorphism monoid $(\text{End}(X), \circ)$. We say that the space $X$ has a unique endomorphism monoid if $\text{End}(X) \cong \text{End}(Y)$ as monoids, for some space $Y$, then the spaces $X$ and $Y$ are […]

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## Prove that √det(ATA)=॥xｘy॥

If x,y ∈ R3 and A is a 2 by 3 matrix whose columns are x and y. Is there a way to solve this without solving the square root of the det?

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## Folland Exercise 4 chapter 5

*If $X$, $Y$ are normed vector spaces the map (T,x)$\rightarrow$Tx is continuous from $L(X,Y)\times x$ to $Y$. ( That is, if $T_n\rightarrow T$ and $x_n\rightarrow x$ then $T_nx_n\rightarrow Tx$ My professor told me to use $\epsilon$ proof. So here is the proof: $\forall\epsilon>0$ $\exists N_1\in\Bbb N$ s.t $\forall n\geq N_1$ $||T_n-T||<\epsilon/(2(||x||+1))$. $\forall\epsilon>0$ $\exists N_2\in\Bbb N$ […]