Related papers: Non-archimedean topological monoids

Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…

For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism…

We study algebraic structure of the $\lambda$-polycyclic monoid $P_{\lambda}$ and its topologizations. We show that the $\lambda$-polycyclic monoid for an infinite cardinal $\lambda\geqslant 2$ has similar algebraic properties so has the…

Denote by $\mathcal{NA}$ and $\mathcal{MA}$ the ideals of null-additive and meager-additive subsets of~$2^\omega$, respectively. We prove in ZFC that $\mathrm{add}(\mathcal{NA})=\mathrm{non}(\mathcal{NA})$ and introduce a new (Polish)…

Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish…

The free monoid $A^*$ on a finite totally ordered alphabet $A$ acts at the left on columns, by Schensted left insertion. This defines a finite monoid, denoted $Styl(A)$ and called the stylic monoid. It is canonically a quotient of the…

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological…

A notion of {\em normal submonoid} of a monoid $M$ is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set $\mathsf{NorSub}(M)$ of normal submonoids of $M$ is a complete lattice. Joins are…

We find anti-isomorphic submonoids $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ of the bicyclic monoid $\mathscr{C}(a,b)$ with the following properties: every Hausdorff left-continuous (right-continuous) topology on…

For every countable structure $M$ we construct an $\aleph_0$-stable countable structure $N$ such that $Aut(M)$ and $Aut(N)$ are topologically isomorphic. This shows that it is impossible to detect any form of stability of a countable…

We initiate the study of higher dimensional topological finiteness properties of monoids. This is done by developing the theory of monoids acting on CW complexes. For this we establish the foundations of $M$-equivariant homotopy theory…

The paper fills gaps in knowledge about Kuratowski operations which are already in the literature. The Cayley table for these operations has been drawn up. Techniques, using only paper and pencil, to point out all semigroups and its…

We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed…

We identify four countable topological spaces $S_2$, $S_1$, $S_D$, and $S_0$ which serve as canonical examples of topological spaces which fail to be quasi-Polish. These four spaces respectively correspond to the $T_2$, $T_1$, $T_D$, and…

We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid…

We completely classify all neutral or costandard elements in the lattice $\mathbb{MON}$ of all monoid varieties. Further, we prove that an arbitrary upper-modular element of $\mathbb{MON}$ except the variety of all monoids is either a…

We introduce the class of strongly sofic monoids. This class of monoids strictly contains the class of sofic groups and is a proper subclass of the class of sofic monoids. We define and investigate sofic topological entropy for actions of…

We introduce a new topological generalization of the $\sigma$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^{\omega}\omega$ by $^{\kappa}\kappa$, for $\kappa$ regular uncountable, or replaced countable…

A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology.…

It is shown that a topological group G is topologically isomorphic to the isometry group of a (complete) metric space iff G coincides with its G-delta-closure in the Rajkov completion of G (resp. if G is Rajkov-complete). It is also shown…