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Relative Homotopy in Relational Structures

Published online by Cambridge University Press:  20 November 2018

P. J. Witbooi
P. J. Witbooi*
Affiliation:
University of the Western Cape, Private Bag X17, 7535 Bellville, South Africa e-mail: pwitbooi@uwc.ac.za
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Abstract

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The homotopy groups of a finite partially ordered set (poset) can be described entirely in the context of posets, as shown in a paper by $\text{B}$ . Larose and $\text{C}$ . Tardif. In this paper we describe the relative version of such a homotopy theory, for pairs $\left( X,\,A \right)$ where $X$ is a poset and $A$ is a subposet of $X$ . We also prove some theorems on the relevant version of the notion of weak homotopy equivalences for maps of pairs of such objects. We work in the category of reflexive binary relational structures which contains the posets as in the work of Larose and Tardif.

Keywords

55Q0554A0518B30binary reflexive relational structurerelative homotopy groupexact sequencelocally finite spaceweak homotopy equivalence

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 310 - 320
Copyright
Copyright © Canadian Mathematical Society 2008

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