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Neil Strickland
Neil Strickland
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What properties should $C(M,\mathbb{R})$ hashave when $M$ is a $n$-dimensional manifold?

Optimzing latex expressions.
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edit approved Jun 30, 2021 at 20:18
vitamin d
edit approved Jun 30, 2021 at 20:18
vitamin d
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What properties should $C(M,\mathbb{R})$ has when $M$ is a n$n$-dimensional manifold?

Let $M$ be a n-dimensional manifold, $C(M,\mathbb{R})$ be the function space of continuous function from $M$ to $\mathbb{R}$. What kind of properties should $C(M,\mathbb{R})$ has, to reflect the manifold structure?

Denote a L-shape line be $X$, we know it is not a manifold, but what difference can we observe from the algebras of continuous function compared to circle? i.e. What properties does $C(M,\mathbb{R})$ has and $C(X,\mathbb{R})$ does not? In this case their topological dimension is the same, so they should have same stable rank in terms of C*$C^*$-algebras.

What properties should $C(M,\mathbb{R})$ has when $M$ is a n-dimensional manifold?

Let $M$ be a n-dimensional manifold, $C(M,\mathbb{R})$ be the function space of continuous function from $M$ to $\mathbb{R}$. What kind of properties should $C(M,\mathbb{R})$ has, to reflect the manifold structure?

Denote a L-shape line be $X$, we know it is not a manifold, but what difference can we observe from the algebras of continuous function compared to circle? i.e. What properties does $C(M,\mathbb{R})$ has and $C(X,\mathbb{R})$ does not? In this case their topological dimension is the same, so they should have same stable rank in terms of C*-algebras.

What properties should $C(M,\mathbb{R})$ has when $M$ is a $n$-dimensional manifold?

Let $M$ be a n-dimensional manifold, $C(M,\mathbb{R})$ be the function space of continuous function from $M$ to $\mathbb{R}$. What kind of properties should $C(M,\mathbb{R})$ has, to reflect the manifold structure?

Denote a L-shape line be $X$, we know it is not a manifold, but what difference can we observe from the algebras of continuous function compared to circle? i.e. What properties does $C(M,\mathbb{R})$ has and $C(X,\mathbb{R})$ does not? In this case their topological dimension is the same, so they should have same stable rank in terms of $C^*$-algebras.

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Ken.Wong
Ken.Wong
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What properties should $C(M,\mathbb{R})$ has when $M$ is a n-dimensional manifold?

Let $M$ be a n-dimensional manifold, $C(M,\mathbb{R})$ be the function space of continuous function from $M$ to $\mathbb{R}$. What kind of properties should $C(M,\mathbb{R})$ has, to reflect the manifold structure?

Denote a L-shape line be $X$, we know it is not a manifold, but what difference can we observe from the algebras of continuous function compared to circle? i.e. What properties does $C(M,\mathbb{R})$ has and $C(X,\mathbb{R})$ does not? In this case their topological dimension is the same, so they should have same stable rank in terms of C*-algebras.