# Tagged Questions

**1**

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**1**answer

153 views

### Final topology of surjective linear map on Banach space

Let $L:X\rightarrow Y$ be a surjective linear map from Banach space $(X,||\cdot||_X)$ to vector space $Y$ and denote with $\tau_L$ the final topology on $Y$ induced by $T$.
Is $\tau_L$ equivalent ...

**0**

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**1**answer

82 views

### Banach Isomomorphic Cts Fucntion Algebras for two Non-Homeomorphic Top Spaces?

Can anyone provide me with an example of two non-homeomorphic locally-compact Hausdorff spaces $X$ and $Y$, such that $C(X)$ and $C(Y)$ are isomorphic as Banach algebras. Clearly, the ...

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**0**answers

214 views

### Is there Ultracoproduct-like construction for topological spaces in general?

In
http://arxiv.org/pdf/math/9704205.pdf
they define the ultracoproduct of a sequence of compact Hausdorff spaces, $\sum_\mathcal{U}X_i$ along an ultrafilter $\mathcal{U}$ as the Wallman-Frink ...

**1**

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**1**answer

194 views

### Agreement of two topologies on a linear space

I'm dealing with the formalism of an abstract Wiener space, and I'm not sure if two relevant topologies coincide.
Let $X$ be a topological vector space, and let $X^*$ be its dual space of continuous ...

**3**

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**1**answer

136 views

### Algebras with countable chains only

Is there an example of an uncountable Boolean algebra $B$ in which every chain is countable and such that $\ell_\infty$ embeds into the Banach space $C(\mbox{Stone }B)$? The latter requirement is not ...

**1**

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**1**answer

130 views

### How (and when) to factor a function defined on a product of metric spaces?

Suppose we have a set of regular functions defined on a product of metric spaces, for instance the Banach space of the smooth functions from $\mathbb R^n$ to $\mathbb C$. We know, thanks to the Taylor ...

**3**

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**1**answer

331 views

### Determining continuous functions on Banach spaces

Let $X$ be a real Banach space.
For a continuous (not necessarily linear) function $g:X \to \mathbb{R}$ and a family $\mathcal{F} \subseteq X^*$, we´ll say that $\mathcal{F}$ determines $g$ if ...

**5**

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**3**answers

986 views

### A criterion for the sum of two closed sets to be closed ?

Let $V$ and $I$ be two closed subsets of a Banach space $A$.
The set $V$ is a convex cone, and $I$ is a linear subspace of $A$. I also know that $V\cap I=\{0\}$.
I would like to know whether $I+V$ ...

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**2**answers

280 views

### ED compact $K$ such that $C(K)$ is not a dual Banach space

Almost every mathematician working in von Neumann algebras says that there are certainly extremely disconnected compact spaces $K$ such that $C(K)$ is not a dual space (they are not hyperstonean). ...

**0**

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**2**answers

400 views

### “Exotic” Banach spaces of sequences

Does there exist a linear subspace of $\mathbb C ^{\mathbb N}$ that can be endowed a Banach space topology that is not finer than the locally convex topology of pointwise convergence?
Best,
Martin

**1**

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**2**answers

572 views

### Are coordinate functions on topological vector spaces always continuous?

Let $V$ be a Hausdorff locally convex topological vector space over the field $\mathbb{K}$.
Let $B$ be a subset of $V$ such that
$\;$ for all functions $c : B\to \mathbb{K}$, if ...

**6**

votes

**0**answers

1k views

### Weak lower semi-continuity

Which conditions assure the weak lower semicontinuity of, say, an integral functional of the type
$F(u):=\int_\Omega f(u(x),Du(x))dx$ on $W^{1,2}(\Omega,\mathbb{R}^N)$ for a bounded, if you will ...

**3**

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**3**answers

381 views

### Shape of long sequences in C(ω_1)

Apologies for the vague title - I couldn't come up with a single sentence that summarised this problem well. If you can, please edit or suggest a better one!
This question is also rather specific and ...

**1**

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**6**answers

2k views

### Cone in a metric space

Hi everybody,
We know the definition of a cone in a Real Banach Space.
I want to know if there is any definition for a cone in an abstract metric space.
Have you ever seen such definition anywhere?
...