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On unitary extensions and unitary completions of topological monoids

100%

Averbukh B. G.

Topological Algebra and its Applications

2016

tom 4

nr 1

The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.

On finest unitary extensions of topological monoids

100%

Averbukh B. G.

Topological Algebra and its Applications

2015

tom 3

nr 1

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.

On unitary Cauchy filters on topological monoids

100%

Averbukh B. G.

Topological Algebra and its Applications

2013

tom 1

46-59

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.

Ograniczanie wyników

3 Topological Algebra and its Applications

3 Averbukh B. G.

1 2016

1 2015

1 2013

Wyniki wyszukiwania

On unitary extensions and unitary completions of topological monoids

On finest unitary extensions of topological monoids

On unitary Cauchy filters on topological monoids