# On finest unitary extensions of topological monoids

Topological Algebra and its Applications (2015)

- Volume: 3, Issue: 1, page 1-10, electronic only
- ISSN: 2299-3231

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topBoris G. Averbukh. "On finest unitary extensions of topological monoids." Topological Algebra and its Applications 3.1 (2015): 1-10, electronic only. <http://eudml.org/doc/268686>.

@article{BorisG2015,

abstract = {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.},

author = {Boris G. Averbukh},

journal = {Topological Algebra and its Applications},

keywords = {topological monoid; Cauchy space; completion},

language = {eng},

number = {1},

pages = {1-10, electronic only},

title = {On finest unitary extensions of topological monoids},

url = {http://eudml.org/doc/268686},

volume = {3},

year = {2015},

}

TY - JOUR

AU - Boris G. Averbukh

TI - On finest unitary extensions of topological monoids

JO - Topological Algebra and its Applications

PY - 2015

VL - 3

IS - 1

SP - 1

EP - 10, electronic only

AB - 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.

LA - eng

KW - topological monoid; Cauchy space; completion

UR - http://eudml.org/doc/268686

ER -

## References

top- [1] B. G. Averbukh, On unitary Cauchy filters on topological monoids, Topol. Algebra Appl., 1 (2013), 46-59. Zbl1288.22001
- [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] Zbl0428.54018
- [3] H.H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann. 176 (1968), 334-341. MR 37#874. Zbl 155.50302 Zbl0155.50302
- [4] D.C. Kent, G.D. Richardson, Regular completions of Cauchy spaces, Pacific Journal of mathematics 51, No. 2 (1974), 483- 490. [Crossref] Zbl0291.54024
- [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] Zbl0675.54004
- [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. Zbl0195.24402
- [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] Zbl0960.54017
- [9] N. Rath, Completions of Filter Semigroups, Acta Math. Hungar. 107 (1-2) (2005), 45-54. Zbl1092.54008
- [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. Zbl0213.49601

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