# Tagged Questions

**2**

votes

**1**answer

192 views

### “Nice” functions on infinite-dimensional space of germs of continuous functions at a point

Consider set of all germs of continuous functions at some point.
Question: What are some functions ("any/nice/constructive/whatever") from this set to R (reals) ? (Except evalution at point and made ...

**6**

votes

**2**answers

264 views

### function that is the average of affine transformations of itself

Consider the function $f : \mathbb{R} \to [-1,1]$ with
$$
f(x) = \begin{cases}
-1 & x \le -1 \\
+1 & x \ge +1 \\
\frac{f(\frac32 (x-\frac13)) + f(\frac32 ...

**1**

vote

**0**answers

182 views

### Classification of Self similar sets

I am looking at self similar sets in $\mathbb{C}$ defined as the fixed set or a sequence of contractions or an iterated function system. I am currently trying to classify these sets by how they are ...

**2**

votes

**1**answer

609 views

### Hausdorff dimension of graphs .

Is there an easy way to calculate the Hausdorff dimension of the graph of a real "elementary" function, like $f(x)=\sin(1/x)$ ?