On factorization of maps through τX

Błaszczyk, Aleksander; Mioduszewski, J.

doi:10.4064/cm-23-1-45-52

Cited by 12 publications

(4 citation statements)

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“…A subset A of X is far from the remainder (f.f.r.) [1] in X if for every free open ultrafilter *fr on X, there is open Ue^ such that c\ x U f] A = 0; a subset A of X is rigid in X [3] if for every filter base ^ on X such that Ann {<&ΘF\ Fe^~} = 0, there is open set U containing A and Fe ^ such that clU Π F = 0. The following facts are used in the sequel:…”

Section: And Called H-closed Relative To X An Open Filter Is a Filtementioning

confidence: 99%

𝜃-closed subsets of Hausdorff spaces

Dickman¹,

Porter²

1975

Pacific J. Math.

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Section: And Called H-closed Relative To X An Open Filter Is a Filtementioning

confidence: 99%

𝜃-closed subsets of Hausdorff spaces

Dickman¹,

Porter²

1975

Pacific J. Math.

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“…It is shown in [7] that for a proper subset A of a space X , part (b) of the above result fails, while we shall show (see Example 4.15) that part (a) of the above result need not be true for a proper subset of a space X .…”

Section: Results 42 For the Whole Space X The Notions Of (A) S(θ )-mentioning

confidence: 85%

On certain missing links in the hierarchy of some compact-like covering properties

Mukherjee

Sinha

2016

Afr. Mat.

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It is found in the literature that several compact-like covering properties have been introduced and studied by different researchers. However, there are certain missing links in the implication-diagram among all these. The aim of this paper is to fill up these gaps by introducing three new types of covering properties in terms of semiopen and preopen sets, thereby providing a balanced and complete diagram in respect of the hierarchy of the existing and the introduced types of properties. The latter types of covering properties are characterized, and studied to some extent, and a number of non-trivial examples are given to justify non-implications. Finally, certain conditions are worked out under which such reverse implications may hold.

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“…Several other authors independently have considered variations and generalizations of the idea of a perfect map: For example, [2] considers (in Hausdorff spaces) maps which preserve remainder in the Katëtov //-closed extension; [9] gives a categorical generalization and shows that in Tych, when y D^, the definition agrees with 2.1; [16] Proof. Let / : A -» S (E J^.…”

Section: Proposition Given S/ Let R and R' Denote The Functors For mentioning

confidence: 99%

Perfect Maps and Epi-Reflective Hulls

Hager

1975

Can. j. math.

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The main theorems concern the relation between the - compact spaces and the -regular spaces, and their analogues in uniform spaces. In either of the categories of Tychonoff spaces or uniform spaces, let be a class of spaces, let be the epi-reflective hull of se (closed subspaces of products of members of ), let be the “onto-reflective” hull of (all subspaces of products of members of ), and let r and o be the associated functors. Let be the class of spaces which admit a perfect map into a member of . Then, is epi-reflective (and in Tych, = but in Unif, the equality fails); call the functor p.

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On factorization of maps through τX

Cited by 12 publications

References 0 publications

𝜃-closed subsets of Hausdorff spaces

𝜃-closed subsets of Hausdorff spaces

On certain missing links in the hierarchy of some compact-like covering properties

Perfect Maps and Epi-Reflective Hulls

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