# Questions tagged [topological-algebras]

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15
questions

**-1**

votes

**1**answer

94 views

### Topological connected eccentrics, not homeomorphic to commutative Lie groups

An eccentric is a universal algebra $\ (X\ \sigma\ \lambda\ \rho)\ $ such that operations
$\ \sigma\ \lambda\ \rho\,:\,X\times X\to X\ $ satisfy:
$\quad \forall_{x\ y\,\in X}\quad \lambda(\sigma(x\ y)...

**2**

votes

**1**answer

97 views

### Measurability of the product on particular topological vector spaces

Let $X$ be a topological vector space. Let us say that $X$ has property P if there exists a sequence of closed subsets $\{X_n\}$ such that
1- $X=\bigcup X_n$
2- The relative topology is both ...

**6**

votes

**0**answers

125 views

### m-systems and n-systems in topological rings

Note that throughout rings have a multiplicative identity and are not necessarily commutative
Definition: Let $R$ be a ring and let $M\subseteq R$. Then, $M$ is an m-system iff for every $x,y\in ...

**1**

vote

**0**answers

63 views

### Working in coordinates with topologies on the algebra of continuous functions

Let $X$ be a Hausdorff completely regular topological space, and let $C_b (X)$ be its algebra of continuous bounded functions. Endow $C_b (X)$ with a topology given by some seminorms, that contains ...

**7**

votes

**3**answers

694 views

### Can the topological algebra of analytic functions be endowed with a norm that defines the natural topology?

Right, so in my research in complex analysis I was puzzled by this question which may have a simple approachable answer that eludes me, but I am truly itching to find out and in need of it so I am ...

**2**

votes

**1**answer

220 views

### Is torsion submodule of a $p$-adically complete and separated $\mathbb{Z}_{p}$-module closed?

I was asking to myself the following question. Consider a $p$-adically complete and separated topological algebra $R$ over $\mathbb{Z}_{p}$. As $\mathbb{Z}_{p}$ is a domain, we know that the $\mathbb{...

**6**

votes

**0**answers

111 views

### Categorical description of dense homomorphisms of topological algebras

Let $A$ and $B$ be topological associative algebras (no matter, in which sense, for example, over $\mathbb C$, with identity, and with separately continuous multiplication). Let us say that a (...

**3**

votes

**0**answers

94 views

### How Universal is the Topological $\mathbb K$-algebra $C(\Omega, \mathbb K)$?

For $\Omega$ an arbitrary set the family $C(\Omega, \mathbb K)$ of all functions $\Omega \to \mathbb K$ becomes a complete topological $\mathbb K$-algebra under the topology of uniform convergence. ...

**10**

votes

**2**answers

531 views

### Definition of internal field objects

Let $\mathcal{C}$ be a category with finite limits and a strictly initial object $\mathbf{0}$. The final object is denoted by $\mathbf{1}$. I propose the following definition of a field object ...

**5**

votes

**1**answer

164 views

### When does topological homogeneity imply algebraic homogeneity? Pseudo-arc and Hilbert cube

Knaster's pseudo-arc and Hilbert cube are topologically homogeneous continua. The easier question is: do these spaces admit a topological group structure? (I am sure that the answer is negative). Thus ...

**2**

votes

**2**answers

185 views

### Generic topology on a field

I'm wondering if there is some generic topology that can be put on any field of characteristic zero which is similar to those induced by a norm on the field. I know that for vector spaces you can take ...

**5**

votes

**0**answers

300 views

### Quotient of complete topological ring

Let $G$ be a complete topological group (meaning that every Cauchy net has a unique limit), and $H\unlhd G$ a closed normal subgroup. If $G$ is first countable (equivalently, metrizable), then $G/H$ ...

**6**

votes

**0**answers

219 views

### Series in topological rings that only converge if almost all summands are zero

While trying to understand a certain topological ring better, I stumbled onto the following question.
Suppose $I$ is a fixed infinite index set, $R$ is a topological ring and $(x_i)_{i\in I}$ is a ...

**7**

votes

**2**answers

3k views

### Completion and Tensor Product of Algebras

Let $A$ be a commutative ring with 1, $I$ an ideal in $A$, $B$ an $A$-algebra. I am trying to prove the following isomorphism of $A$-algebras:
$$ \big( A^* \otimes _A B \big) ^* \cong B^* $$
"$^*$" ...

**5**

votes

**1**answer

314 views

### Entire calculus and clmc algebras

If $\mathcal{A}$ is a complete locally convex (Hausdorff) associative unital algebra (over $\mathbb{C}$) one is interested in defining "transcendental" functions of a given algebra element $a \in \...