On dowker’s theorem

Murad M. Arar

doi:10.17654/gt019010027

On dowker’s theorem

Murad M. Arar

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce a fiberwise version of Dowker’s theorem which states that: If f₁: X₁ →Y₁and f₂: X₂ →Y₂ are any two mappings such that f₁ × f₂: X₁ ×X₂ →Y₁ ×Y₂is closed and f₂: X₂ →Y₂is a compact MT-mapping with at least one infinite fiber, then f₁: X₁ →Y₁ is normal countably paracompact if and only if f₁ × f₂ is normal.

Original language	English
Pages (from-to)	27-40
Number of pages	14
Journal	JP Journal of Geometry and Topology
Volume	19
Issue number	1
DOIs	https://doi.org/10.17654/gt019010027
State	Published - Feb 2016

Keywords

Dowker’s theorem
Fiberwise
Mapping
Paracompact

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10.17654/gt019010027

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title = "On dowker{\textquoteright}s theorem",

abstract = "In this paper, we introduce a fiberwise version of Dowker{\textquoteright}s theorem which states that: If f1: X1 →Y1and f2: X2 →Y2 are any two mappings such that f1 × f2: X1 ×X2 →Y1 ×Y2is closed and f2: X2 →Y2is a compact MT-mapping with at least one infinite fiber, then f1: X1 →Y1 is normal countably paracompact if and only if f1 × f2 is normal.",

keywords = "Dowker{\textquoteright}s theorem, Fiberwise, Mapping, Paracompact",

author = "Arar, \{Murad M.\}",

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AB - In this paper, we introduce a fiberwise version of Dowker’s theorem which states that: If f1: X1 →Y1and f2: X2 →Y2 are any two mappings such that f1 × f2: X1 ×X2 →Y1 ×Y2is closed and f2: X2 →Y2is a compact MT-mapping with at least one infinite fiber, then f1: X1 →Y1 is normal countably paracompact if and only if f1 × f2 is normal.

KW - Dowker’s theorem

KW - Fiberwise

KW - Mapping

KW - Paracompact

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JF - JP Journal of Geometry and Topology

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ER -

On dowker’s theorem

Abstract

Keywords

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