Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Method of construction of topologies on any finite set
Authors: Arnautov Vladimir
Keywords: finite set, topologies, lattice of all open sets, atoms, quasiatoms.
– 0.15 Mb
Keywords: finite set, topologies, lattice of all open sets, atoms, quasiatoms.
Abstract
Let a topology τ be defined on a finite set. We give the definition of quasiatoms in the lattice (τ, ⊆) and study their properties. For any splitting of a finite set X into k subsets we give a method of constructing any topology on the set X for which this splitting is the set of all quasiatoms and the weight of this topological space is equal to k.Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str. Chişinău MD-2028, Moldova
E-mail:
Academy of Sciences of Moldova
5 Academiei str. Chişinău MD-2028, Moldova
E-mail:
Fulltext
– 0.15 Mb
Contents
- Basic cohomology attached to a basic function of foliated manifolds
- Isohedral tilings on Riemann surfaces of genus 2
- Method of construction of topologies on any finite set
- Generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree
- On partial inverse operations in the lattice of submodules
- The Generalized Lagrangian Mechanical Systems
- Cubic systems with seven invariant straight lines of configuration (3,3,1)
- The Ricci-flat spaces related to the Navier-Stokes equations
