Completion functors for Cauchy spaces

Frič, Roman; Kent, D. C.

doi:10.1155/s0161171279000442

Cited by 19 publications

(17 citation statements)

References 6 publications

(10 reference statements)

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“…The completion of Cauchy spaces is already well known and familiar to most of us. In fact, since Keller [5] introduced the axiomatic definition of Cauchy spaces a very rich and extensive completion theory has been developed for Cauchy spaces during the last three decades [2,3,7,10,12]. It seems that Cauchy space rather than uniform convergence space is a natural generalization of completion of uniform space.…”

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confidence: 99%

Completion of a Cauchy space without the T₂‐restriction on the space

Rath

1999

International Journal of Mathematics and Mathematical Sciences

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Abstract. A completion of a Cauchy space is obtained without the T 2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called s-maps form a subcategory CHY of CHY. A completion functor is defined for this subcategory. The completion subcategory of CHY turns out to be a bireflective subcategory of CHY . This theory is applied to obtain a characterization of Cauchy spaces which allow regular completion.

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confidence: 99%

Completion of a Cauchy space without the T₂‐restriction on the space

Rath

1999

International Journal of Mathematics and Mathematical Sciences

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“…Each Cauchy space has many completions which have been studied in papers of many authors (see [2][3][4][5][6][7][8][9][10][11]). The most important of them is perhaps the Wyler completion possessing the universal property over other completions.…”

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confidence: 99%

On finest unitary extensions of topological monoids

Averbukh

2015

Topological Algebra and Its Applications

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“…Without repeating the relevant definitions here, we remark that, in the terminology of [5], the functor K: COCS OCON, defined by K(X, , C) (X*, *, C*) is an order-strict completion functor, and consequently that COCS is a completion subcategory of OCS. We shall henceforth refer to ((X*, @*, C*), j) as the fine ordered completion of (X, , C), and K will be called the fine ordered completion functor.…”

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confidence: 99%