Algebraic & Geometric Topology

Extensions of maps to the projective plane

Jerzy Dydak and Michael Levin

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Abstract

It is proved that for a 3–dimensional compact metrizable space X the infinite real projective space P is an absolute extensor of X if and only if the real projective plane P2 is an absolute extensor of X (see Theorems 1.2 and 1.5).

Article information

Source
Algebr. Geom. Topol., Volume 5, Number 4 (2005), 1711-1718.

Dates
Received: 1 June 2005
Accepted: 7 November 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796496

Digital Object Identifier
doi:10.2140/agt.2005.5.1711

Mathematical Reviews number (MathSciNet)
MR2186116

Zentralblatt MATH identifier
1094.55003

Subjects
Primary: 55M10: Dimension theory [See also 54F45]
Secondary: 54F45: Dimension theory [See also 55M10]

Keywords
cohomological extensional dimensions projective spaces

Citation

Dydak, Jerzy; Levin, Michael. Extensions of maps to the projective plane. Algebr. Geom. Topol. 5 (2005), no. 4, 1711--1718. doi:10.2140/agt.2005.5.1711. https://projecteuclid.org/euclid.agt/1513796496


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References

  • M Cencelj, A N Dranishnikov, Extension of maps to nilpotent spaces. II, Topology Appl. 124 (2002) 77–83
  • M Cencelj, A N Dranishnikov, Extension of maps to nilpotent spaces. III, Topology Appl. 153 (2005) 208–212
  • A N Dranishnikov, On a problem of P S Aleksandrov, Mat. Sb. (N.S.) 135(177) (1988) 551–557, 560
  • A N Dranishnikov, Extension of mappings into CW-complexes, Mat. Sb. 182 (1991) 1300–1310
  • A N Dranishnikov, Basic elements of the cohomological dimension theory of compact metric spaces, Topology Atlas (1999)
  • M Levin, Some examples in cohomological dimension theory, Pacific J. Math. 202 (2002) 371–378
  • G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer-Verlag, New York (1978)