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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...

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

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Displaying 561 – 580 of 925

Principal fibre bundles with structural Lie groupoid.

Principle of equicontinuity for topological groups

Probability measures on compact semitopological semigroups

Problems 44 and 39 on compact semilattices.

Problems about semitopological semigroups.

Problems on compact emilattices.

Problems on semigroups and control.

Product decomposition of idempotent measures on compact semigroups

Productivity of the Zariski topology on groups

Products of coarse convergence groups

Products of Minimal Abelian Groups.

Products of protopological groups.

Products of threads.

Products of topological spaces represent any semigroup (Preliminary communication)

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

Profinite relational structures

Projective Limits of Unitary Representations.

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

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

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

Currently displaying 561 – 580 of 925