Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 121-138 |
| Seitenumfang | 18 |
| Fachzeitschrift | Topology Proceedings |
| Jahrgang | 45 |
| Publikationsstatus | Veröffentlicht - 2015 |
Abstract
We consider classes Τ of topological spaces (referred to as Τ-spaces) that are stable under continuous images and frequently under arbitrary products. A local Τ -space has for each point a neighborhood base consisting of subsets that are Τ -spaces in the induced topology. A general necessary and sufficient criterion for a product of topological spaces to be a local Τ -space in terms of conditions on the factors enables one to establish a broad variety of theorems saying that a product of spaces has a certain local property (like local compactness, local sequential compactness, local σ-compactness, local connectedness etc.) if and only if each factor has that local property, almost all have the corresponding global property, and not too many factors fail a suitable additional condition. Many of the results admit a point-free formulation; a look at sum decompositions into components of spaces with local properties yields product decompositions into indecomposable factors for certain classes of frames like completely distributive lattices or hypercontinuous frames.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Geometrie und Topologie
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in: Topology Proceedings, Jahrgang 45, 2015, S. 121-138.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Tychonoff-like product theorems for local topological properties
AU - Brandhorst, Simon
AU - Erné, Marcel
PY - 2015
Y1 - 2015
N2 - We consider classes Τ of topological spaces (referred to as Τ-spaces) that are stable under continuous images and frequently under arbitrary products. A local Τ -space has for each point a neighborhood base consisting of subsets that are Τ -spaces in the induced topology. A general necessary and sufficient criterion for a product of topological spaces to be a local Τ -space in terms of conditions on the factors enables one to establish a broad variety of theorems saying that a product of spaces has a certain local property (like local compactness, local sequential compactness, local σ-compactness, local connectedness etc.) if and only if each factor has that local property, almost all have the corresponding global property, and not too many factors fail a suitable additional condition. Many of the results admit a point-free formulation; a look at sum decompositions into components of spaces with local properties yields product decompositions into indecomposable factors for certain classes of frames like completely distributive lattices or hypercontinuous frames.
AB - We consider classes Τ of topological spaces (referred to as Τ-spaces) that are stable under continuous images and frequently under arbitrary products. A local Τ -space has for each point a neighborhood base consisting of subsets that are Τ -spaces in the induced topology. A general necessary and sufficient criterion for a product of topological spaces to be a local Τ -space in terms of conditions on the factors enables one to establish a broad variety of theorems saying that a product of spaces has a certain local property (like local compactness, local sequential compactness, local σ-compactness, local connectedness etc.) if and only if each factor has that local property, almost all have the corresponding global property, and not too many factors fail a suitable additional condition. Many of the results admit a point-free formulation; a look at sum decompositions into components of spaces with local properties yields product decompositions into indecomposable factors for certain classes of frames like completely distributive lattices or hypercontinuous frames.
KW - (Local) Τ -space
KW - (Locally) compact
KW - (Locally) connected
KW - Product space
UR - http://www.scopus.com/inward/record.url?scp=85016245541&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85016245541
VL - 45
SP - 121
EP - 138
JO - Topology Proceedings
JF - Topology Proceedings
SN - 0146-4124
ER -