# Tagged Questions

**-2**

votes

**0**answers

36 views

### Bounding and continuity in Banach spaces [closed]

Prove that if mapping in Banach space is bounded, it is continuous.

**3**

votes

**3**answers

295 views

### Cardinality of $C^*([0,1])$ [closed]

What is the cardinality of the continuous dual of $C([0,1])$ (the set of continuous functions from $[0,1]\to \mathbb{R}$)?

**3**

votes

**1**answer

151 views

### A functional equality

I don't know if this is known, but I was fiddling around with this equality :
$$f:(-1,1)\to (-1,1)\quad \text{satisfies}\quad(f(z)+1)^s=\sum_{j=0}^{\infty}\dbinom{s}{j}f(z^k)
\quad \forall z\in ...

**1**

vote

**0**answers

71 views

### If an upper semicontinuous multivalued map is compact on a set, is it compact on the boundary as well?

I have stumbled upon the following problem during my research:
Let $X$ and $Y$ be Banach spaces, $K\subset X$ nonempty, $F:\overline{K}\rightarrow 2^{Y}$ an upper semicontinuous multivalued map with ...

**0**

votes

**0**answers

178 views

### Continuity of a function

Let $f\in L^2(\mathbb{R}^3)$ with compact suppport and $z\in\mathbb{C}$. Is the following function continuous for $z\in Q = \{ z : \Re z\in [a,b], \Im \sqrt{z} \in (0,1] \}$:
$$ ...