Continuous convergence in<i>C</i>(<i>X</i>)

Kent, D. C.; McKennon, Kelly; Richardson, G. D.; Schröder, M.

doi:10.2140/pjm.1974.52.457

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Results Henceforth Let1

Relative Complements1

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1977

1991

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Cited by 23 publications

(12 citation statements)

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“…Hausdorff c-embedded spaces have also been studied intensively by E. Binz [5], D. C. Kent et al [22] and M. Schroder [30]. Hausdorff spaces do not form a topological category, only a closely related kind of category studied by L. D. Nel [27].…”

Section: Results Henceforth Letmentioning

confidence: 99%

Cartesian closed topological hulls

Herrlich¹,

Nel²

1977

Proc. Amer. Math. Soc.

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Abstract.It is shown in this paper that if a concrete category 31 admits embedding as a full finitely productive subcategory of a cartesian closed topological (CCT) category, then St admits such embedding into a smallest CCT category, its CCT hull. This hull is characterized internally by means of density properties and externally by means of a universal property. The problem is posed of whether every topological category has a CCT hull.

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Section: Results Henceforth Letmentioning

confidence: 99%

Cartesian closed topological hulls

Herrlich¹,

Nel²

1977

Proc. Amer. Math. Soc.

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“…If r is Hausdorff and u-regular, then q,r has the same properties from (i) and (viii) so by [6], q,r is C-embedded if r is C-embedded. COROLLARY 2.3: (i) If r is the finest first countable structure coarser than r, then (q,r) q,r for every convergence structure q.…”

Section: Relative Complementsmentioning

confidence: 93%

Properties of complements in the lattice of convergence structures

Riecke

1980

International Journal of Mathematics and Mathematical Sciences

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“…A space is defined to be co-regular if cl^'S -» x whenever S -> x. It is shown in [6] that a space X is c-embedded (see [1], [2]) iff X is co-regular and pseudotopological and has enough continuous real-valued functions to separate points. Proof.…”

mentioning

confidence: 99%

“…Examples are given in [2] and [6] of Hausdorff topological spaces which are co-regular but not completely regular. Furthermore, examples abound of regular spaces which are not co-regular.…”

mentioning

confidence: 99%