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Uniform topology onEQ-algebras

100%

Yang J., Long Xin X., He P. F.

Open Mathematics

2017

tom 15

nr 1

354-364

In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.

On unitary Cauchy filters on topological monoids

76%

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

1 Open Mathematics

1 Topological Algebra and its Applications

1 Averbukh B. G.

1 He P. F.

1 Long Xin X.

1 Yang J.

1 2017

1 2013

Wyniki wyszukiwania

Uniform topology onEQ-algebras

On unitary Cauchy filters on topological monoids