Journal of the Mathematical Society of Japan

Extension dimension of a wide class of spaces

Ivan IVANŠIĆ and Leonard R. RUBIN

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Abstract

We prove the existence of extension dimension for a much expanded class of spaces. First we obtain several theorems which state conditions on a polyhedron or $\mathop{\mathrm{CW}}$-complex $K$ and a space $X$ in order that $X$ be an absolute co-extensor for $K$. Then we prove the existence of and describe a wedge representative of extension dimension for spaces in a wide class relative to polyhedra or $\mathop{\mathrm{CW}}$-complexes. We also obtain a result on the existence of a “countable” representative of the extension dimension of a Hausdorff compactum.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 4 (2009), 1097-1110.

Dates
First available in Project Euclid: 6 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1257520501

Digital Object Identifier
doi:10.2969/jmsj/06141097

Mathematical Reviews number (MathSciNet)
MR2588505

Zentralblatt MATH identifier
1182.54023

Subjects
Primary: 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 54C20: Extension of maps

Keywords
absolute co-extensor absolute extensor anti-basis cardinality of a complex CW-complex dd-space ddP-space extension dimension extension theory extension type Hausdorff $\sigma$-compactum polyhedron pseudo-compact $\sigma$-pseudo-compactum $\sigma$-compactum weak extension dimension weight

Citation

IVANŠIĆ, Ivan; RUBIN, Leonard R. Extension dimension of a wide class of spaces. J. Math. Soc. Japan 61 (2009), no. 4, 1097--1110. doi:10.2969/jmsj/06141097. http://projecteuclid.org/euclid.jmsj/1257520501.


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