Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose of the paper is to transfer the classical concepts of a completeness and of a completion into the theory of topological monoids.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Strony
46-59
Opis fizyczny
Daty
otrzymano
2012-11-11
zaakceptowano
2013-10-07
online
2013-12-21
Twórcy
autor
-
Moscow State Forestry University, department of mathematics,
Moscow, Russian Federation, averbuch@gmx.de
Bibliografia
- [1] J.H. Carruth, J.A. Hildebrant, R.J. Koch, The theory of topological semigroups, Pure and Applied Mathematics, MarcelDekker Inc., New York, 1983.
- [2] R. Engelking, General topology. Rev. and compl. ed., Sigma Series in Pure Mathematics, 6., Berlin: HeldermannVerlag, 1989, viii + 529 pp., ISBN 3-88538-006-4, Zbl 0684.54001.
- [3] H.H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann., 1968, 176, 334-341.
- [4] E. Lowen-Colebunders, Function Classes of Cauchy Continuous Maps, Pure and Applied Mathematics, Marcel DekkerInc., New York, 1989.
- [5] D. Marxen, Uniform semigroups, Math. Ann., 1973, 202, 27-36.
- [6] J.F. Ramaley, O. Wyler, Cauchy spaces, http://repository.cmu.edu/math/ 97, 1968.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_taa-2013-0006