The homotopy classes of continuous maps between some non-metrizable manifolds

Baillif, Mathieu

doi:10.1016/j.topol.2004.06.011

Scientific article

English

The homotopy classes of continuous maps between some non-metrizable manifolds

ContributorsBaillif, Mathieu

Published inTopology and its applications, vol. 148, no. 1/3, p. 39-53

Publication date2005

Abstract

Let R be Alexandroff's long ray. We prove that the homotopy classes of continuous maps R^n o R are in bijection with the antichains of P({1,...,n}). The proof uses partition properties of continuous maps R^n o R. We also provide a description of $[X,R]$ for some other non-metrizable manifolds X.

Keywords

Homotopy
Longline
Nonmetrizable manifolds

Classification

arxiv : math.GN

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

BAILLIF, Mathieu. The homotopy classes of continuous maps between some non-metrizable manifolds. In: Topology and its applications, 2005, vol. 148, n° 1/3, p. 39–53. doi: 10.1016/j.topol.2004.06.011

Article

Identifiers

PID : unige:12215
DOI : 10.1016/j.topol.2004.06.011
arXiv : math/0403495v1

Journal ISSN0166-8641

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The homotopy classes of continuous maps between some non-metrizable manifolds

Let R be Alexandroff's long ray. We prove that the homotopy classes of continuous maps R^n o R are in bijection with the antichains of P({1,...,n}). The proof uses partition properties of continuous maps R^n o R. We also provide a description of $[X,R]$ for some other non-metrizable manifolds X.

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