ON THETOPOLOGICAL FUNDAMENTAL GROUPS OF QUOTIENT SPACES

摘要

Let p: X → X/A beaquotient map, where A isasubspaceof X. Westudy 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.