On the Topological Fundamental Groups of Quotient Spaces
AbstractLet p: X → X/A be a quotient map, where A is a subspace of X. We study the conditions under which p ∗(π 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.
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.