On the Topological Fundamental Groups of Quotient Spaces

  • B. Mashayekhy
  • A. Pakdaman
  • H. Torabi Yazd Univ., Iran

Abstract

Let p: XX/A be a quotient map, where A is a subspace of X. We study the conditions under which p 1 qtop (X, x 0)) is dense in π 1 qtop (X/A,∗)), where the fundamental groups have the natural quotient topology inherited from the loop space and p * is a continuous homomorphism induced by the quotient map p. In addition, we present some applications in order to determine the properties of π 1 qtop (X/A,∗). In particular, we establish conditions under which π 1 qtop (X/A,∗) is an indiscrete topological group.
Published
25.12.2013
How to Cite
MashayekhyB., Pakdaman A., and TorabiH. “On the Topological Fundamental Groups of Quotient Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 12, Dec. 2013, pp. 1700–1711, http://umj.imath.kiev.ua/index.php/umj/article/view/2547.
Section
Research articles