Geometric topological completions with universal final lifts

Mielke, M. V.

doi:10.1016/0166-8641(85)90007-0

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Preliminaries2

Dimension 0 In Topological Categories1

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Cited by 8 publications

(3 citation statements)

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“…In this section, we employ initial hulls to extend the notion of dimension zero to a topological category. To this end, recall ( [15]) that each topological functor U : E → B has a left adjoint D : B → E called the discrete functor, and that D(b) is the minimum element in U −1 (b) for each b ∈ B. We denote the collection of all these discrete objects by D(B).…”

Section: Dimension 0 In Topological Categoriesmentioning

confidence: 99%

Initial hulls and zero dimensional objects

Stine¹

2013

Publ. Math. Debrecen

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In this paper we use initial hulls to define zero dimensional (and other) objects in topological categories. In the process we characterize some initial hulls in the category of topological spaces. Examples of zero dimensional objects in several topological categories are given. We relate zero dimensional objects to preT 2 objects via a Theorem which generalizes their relationship for topological spaces.

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Section: Dimension 0 In Topological Categoriesmentioning

confidence: 99%

Initial hulls and zero dimensional objects

Stine¹

2013

Publ. Math. Debrecen

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“…The functor U : E → Set is said to be topological, and E is said to be a topological category over Set, if U is concrete (i.e., faithful and amnestic, (i.e., if U (f ) = id and f is an isomorphism, then f = id )), has small (i.e., set) fibers, and for which every U -source has an initial lift or, equivalently, for which each U -sink has a final lift [19,21,26] or [29].…”

Section: Preliminariesmentioning

confidence: 99%

“…Note that a topological functor U : E → Set is said to be normalized if there is only one structure on the empty set and on a point [2] or [26].…”

Section: Preliminariesmentioning

confidence: 99%