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Let $H$ be a multiplicatively written monoid with identity $1_H$. An atom of $H$ is an element $x \in H \setminus H^\times$ such that $a \ne xy$ for all $x, y \in H \setminus H^\times$, where $H^\tim …

The title has it all. I'm looking for a reference to the following: Q. Let $X, Y, Z$ be finite, non-empty (topological) spaces. When does $X \times Y \cong X \times Z$ imply $Y \cong Z$ (in the ca …

An abelian cancellative semigroup embeds (via a semigroup monomorphism) into an abelian group. What about an abelian cancellative Hausdorff topological semigroup that does not embed (via a monomorphis …

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions. We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ suc …

I apologize for answering my own question. Let $\mathcal K = (\mathbb K, \tau)$ be a T1 topological unital ring, with $\mathbb K = (K, +, \cdot)$, and let $\mathbb K_{(\cdot)}$ be the multiplicative …

Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post). Basically following some ideas of W. Lawvere (but not his termino …

Bonjour/bonsoir à tous et à toutes. I've two questions related to something on which I'm working. I've already tried to discuss about them elsewhere, but it hasn't been fruitful so far. Edit (4 Dic …