Elsevier

Topology and its Applications

Volume 228, 1 September 2017, Pages 47-67
Topology and its Applications

Inverse systems and limits in the category of ditopological plain spaces

https://doi.org/10.1016/j.topol.2017.05.005Get rights and content
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Abstract

In this paper, inverse systems (spectrums) and their inverse limits are described and investigated in the some special subcategories of the category whose objects are ditopological texture spaces and morphisms are the point functions satisfying a compatibility condition, besides bicontinuity. According to that, we especially restrict ourselves to the topological subcategory ifPDitop consisting of point functions as above and ditopological spaces that have plain texturing which is proper, but still quite extensive subclass of texturings. Followed by, so many major properties of inverse systems and limits in the context of category ifPDitop are constructed under the most general conditions. In particular, by considering the full subcategory ifPDicomp of ifPDitop, whose objects are dicompact plain spaces, we acquired various results about the theory of inverse systems consisting of dicompact plain spaces.

MSC

primary
18A22
46M40
54B10
18A35
54B30
18B35
secondary
06D10
18A30
54A05
54E55
18B30

Keywords

Directed set
Inverse system
Inverse (projective) limit
Plain texture
Ditopology
Thread
Bonding map
Product
Equalizer
Real texture
Contravariant functor
Adjoint
Dicompact
Isomorphic categories
Joint topology

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