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The fundamental groupoid as a topological groupoid

Published online by Cambridge University Press:  20 January 2009

R. Brown  and
G. Danesh-Naruie
R. Brown
Affiliation:
School of Mathematics and Computer Science, University College of North Wales, Bangor, Gwynedd. U.K.
G. Danesh-Naruie
Affiliation:
Daneshsaraye-Ali, Roozvelt Ave., Tehran, Iran
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Let X be a topological space. Then we may define the fundamental groupoid πX and also the quotient groupoid (πX)/N for N any wide, totally disconnected, normal subgroupoid N of πX (1). The purpose of this note is to show that if X is locally path-connected and semi-locally 1-connected, then the topology of X determines a “lifted topology” on (πX)/N so that it becomes a topological groupoid over X. With this topology the subspace which is the fibre of the initial point map ∂′: (πX)/N→X over x in X, is the usual covering space of X determined by the normal subgroup N{x} of the fundamental group π(X, x).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 237 - 244
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

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