On universality of finite powers of locally path-connected meager spaces

• Autorzy: Taras Banakh , Robert Cauty
• Języki publikacji: EN

Abstrakty

EN

It is shown that for every integer n the (2n+1)th power of any locally path-connected metrizable space of the first Baire category is 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54B10: Product spaces
• 57N20: Topology of infinite-dimensional manifolds
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 54F45: Dimension theory
• 54D45: Local compactness, σ -compactness

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 1
• Strony: 87-95

Daty

wydano

2005

Twórcy

autor

Taras Banakh

• Department of Mathematics, Lviv National University, Universytetska 1, Lviv 79000, Ukraine
• Instytut Matematyki, Akademia Świętokrzyska, Kielce, Poland

autor

Robert Cauty

• Université Paris VI, UFR 920, Boîte courrier 172, 4, Place, Jussieu, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/cm102-1-8