On finest unitary extensions of topological monoids

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

Abstrakty

EN

We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.

Słowa kluczowe

EN

topological monoid; Cauchy space; completion

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-09-11

zaakceptowano

2014-11-11

online

2015-01-09

Twórcy

autor

Boris G. Averbukh

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

Bibliografia

• [1] B. G. Averbukh, On unitary Cauchy filters on topological monoids, Topol. Algebra Appl., 1 (2013), 46-59.
• [2] R. Fric, D. C. Kent, Completion functors for Cauchy spaces, Int. J. Math. & Math. Sci. 2, No. 4 (1979), 589-604. MR 80#54042. Zbl 428.54018. [Crossref]
• [3] H.H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann. 176 (1968), 334-341. MR 37#874. Zbl 155.50302
• [4] D.C. Kent, G.D. Richardson, Regular completions of Cauchy spaces, Pacific Journal of mathematics 51, No. 2 (1974), 483- 490. [Crossref]
• [5] D. C. Kent, G. D. Richardson, Cauchy completion categories, Canad. Math. Bull. 32, No. 1 (1989), 78-84. MR 90#54007. Zbl 675.54004. [Crossref]
• [6] E. Lowen-Colebunders. Function Classes of Cauchy Continuous Maps, Pure and Applied Mathematics, Marcel Dekker Inc., New York, (1989).
• [7] J. F. Ramaley, O. Wyler, Cauchy spaces, (1968), http://repository.cmu. edu/math/97.
• [8] N. Rath, Completion of a Cauchy space without the T2-restriction on the space, Internat. J. Math. & Math. Sci. 24, No. 3 (2000), 163-172. [Crossref]
• [9] N. Rath, Completions of Filter Semigroups, Acta Math. Hungar. 107 (1-2) (2005), 45-54.
• [10] E. E. Reed, Completions of Uniform Convergence Spaces, Math. Ann. 194 (1971), 83-108. MR 45#1109. Zbl 217.19603. [11] O. Wyler, Ein Komplettierungsfunktor für uniforme Limesräume, Math. Nachr. 46 (1970), 1-12. MR 44#985. Zbl 207.52603.

Identyfikatory

DOI

10.1515/taa-2015-0001