# Tagged Questions

In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind which captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets

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### Ring of germs of smooth functions on $\mathbb{R}^{n}$ in $0$.

First of all, I'm quite new to this theory, so it may be very dumb questions. Sorry for that. Let $R$ be the ring of germs of $C^{\infty}$ functions on $\mathbb{R}^{n}$ in $0$. Let $K$ be the ...
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### Germs and local ring.

I'm having trouble understanding the following argument (which I believe to be somewhat incomplete or flawed). Let $A=C(X)$ be the set of continuous functions from the topological space $X$ to the ...
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### on the infinite power of the maximal ideal

Let $(R,\mathfrak{m})$ be a local ring over a field. Suppose the ring has flat functions, i.e. $\mathfrak{m}^\infty\neq\{0\}$. (The prototype is of course $C^\infty(\Bbb{R}^p,0)$, or a quotient of it, ...
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### question on singularity theory and normal forms of local function germs

Hello I realize this might be a difficult topic but I was just trying to practice for my advanced class on singularities I wanted to compute normal forms for corank 2 singularities of the function ...
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### Is the ring of germs of $C^\infty$ functions at $0$ Noetherian?

I'm considering the property of the ring $R:=C^\infty(\mathbb R)/I$, where $I$ is the ideal of all smooth functions that vanish at a neighborhood of $0$. I find that $R$ is a local ring of which the ...
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### Help with understanding the notation $\mathbb{C}\{f\}$

I am reading an article "Relative Cohomology and volume forms" of J. P. Francoise. Here the author considers the germ of a function $f\colon(\mathbb{C}^n,0) \to (\mathbb{C},0)$, and he speaks of the ...
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