On unitary Cauchy filters on topological monoids

• Autorzy: Boris G. Averbukh
• Języki publikacji: EN

Abstrakty

EN

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

EN

topological monoid; Cauchy space; uniformity

Kategorie tematyczne

• 54E15: Uniform structures and generalizations
• 22A15: Structure of topological semigroups
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2013
• Tom: 1
• Strony: 46-59

Daty

otrzymano

2012-11-11

zaakceptowano

2013-10-07

online

2013-12-21

Twórcy

autor

Boris G. Averbukh

• Moscow State Forestry University, department of mathematics,
  Moscow, Russian Federation

Bibliografia

• [1] J.H. Carruth, J.A. Hildebrant, R.J. Koch, The theory of topological semigroups, Pure and Applied Mathematics, Marcel Dekker Inc., New York, 1983.
• [2] R. Engelking, General topology. Rev. and compl. ed., Sigma Series in Pure Mathematics, 6., Berlin: Heldermann Verlag, 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 Dekker Inc., 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.

Identyfikatory

DOI

10.2478/taa-2013-0006