EuDML | Browse

This paper investigates the productivity of the Zariski topology $ℨ_{G}$ of a group $G$ . If $𝒢 = {G_{i} ∣ i \in I}$ is a family of groups, and $G = \prod_{i \in I} G_{i}$ is their direct product, we prove that $ℨ_{G} \subseteq \prod_{i \in I} ℨ_{G_{i}}$ . This inclusion can be proper in general, and we describe the doubletons $𝒢 = {G_{1}, G_{2}}$ of abelian groups, for which the converse inclusion holds as well, i.e., $ℨ_{G} = ℨ_{G_{1}} \times ℨ_{G_{2}}$ . If $e_{2} \in G_{2}$ is the identity element of a group $G_{2}$ , we also describe the class $Δ$ of groups $G_{2}$ such that $G_{1} \times {e_{2}}$ is an elementary algebraic subset of $G_{1} \times G_{2}$ for every group $G_{1}$ . We show among others, that $Δ$ is stable...

Products of coarse convergence groups

Roman Frič (1988)

Czechoslovak Mathematical Journal

Products of Minimal Abelian Groups.

D.N. Dikranjan, D.B. Shakhmatov (1990)

Mathematische Zeitschrift

Products of protopological groups.

Jones, Julie C. (2001)

International Journal of Mathematics and Mathematical Sciences

Products of threads.

Betty Hinman (1974)

Semigroup forum

Products of topological spaces represent any semigroup (Preliminary communication)

Věra Trnková (1975)

Commentationes Mathematicae Universitatis Carolinae

Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds.

Ludkovsky, S. V., Diarra, B. (2003)

International Journal of Mathematics and Mathematical Sciences

Profinite relational structures

George Janelidze, Manuela Sobral (2008)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Projective Limits of Unitary Representations.

Rudolf A. HIRSCHFELD (1971)

Mathematische Annalen

Projectively Solid Sets and an N-dimensional Piccard's Theorem

Lindgren, W., Szymanski, A. (1998)

Serdica Mathematical Journal

We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property.

Proper groupoids and momentum maps : linearization, affinity, and convexity

Nguyen Tien Zung (2006)

Annales scientifiques de l'École Normale Supérieure

Properties of a pair of functions which generate a dense subsemigroup of S(X).

K.D. jr. Magill (1996)

Semigroup forum

Properties of quasi-invariant measures on topological groups and associated algebras

S.V. Ludkovsky (1999)

Annales mathématiques Blaise Pascal

P-sets and minimal right ideals in ℕ*

W. R. Brian (2015)

Fundamenta Mathematicae

Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...

Currently displaying 21 – 40 of 43

Previous Page 2 Next