# On unitary Cauchy filters on topological monoids

Topological Algebra and its Applications (2013)

- Volume: 1, page 46-59
- ISSN: 2299-3231

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topBoris G. Averbukh. "On unitary Cauchy filters on topological monoids." Topological Algebra and its Applications 1 (2013): 46-59. <http://eudml.org/doc/266770>.

@article{BorisG2013,

abstract = {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.},

author = {Boris G. Averbukh},

journal = {Topological Algebra and its Applications},

keywords = {topological monoid; Cauchy space; uniformity; Topological monoid; -net; unitary uniformity; unitary completeness},

language = {eng},

pages = {46-59},

title = {On unitary Cauchy filters on topological monoids},

url = {http://eudml.org/doc/266770},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Boris G. Averbukh

TI - On unitary Cauchy filters on topological monoids

JO - Topological Algebra and its Applications

PY - 2013

VL - 1

SP - 46

EP - 59

AB - 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.

LA - eng

KW - topological monoid; Cauchy space; uniformity; Topological monoid; -net; unitary uniformity; unitary completeness

UR - http://eudml.org/doc/266770

ER -

## References

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- [3] H.H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann., 1968, 176, 334-341. Zbl0155.50302
- [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. Zbl0234.22003
- [6] J.F. Ramaley, O. Wyler, Cauchy spaces, http://repository.cmu.edu/math/ 97, 1968. Zbl0195.24402

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