The concept of a topology for the fundamental group appears to have originated with Hurewicz (1935), but it has been actively studied only for the last ten years. The classical fundamental group of a pointed topological space X naturally inherits the quotient topology from the space of based loops in X endowed with the compact-open topology. The resulting space, called the topological fundament...

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...

0. Introduction. A subfactorN ⊂M gives rise to a powerful set of invariants that can be approached successfully in several ways. (See, for instance, [B2], [EK], [FRS], [GHaJ], [H], [Iz], [JSu], [Lo1], [Lo2], [Oc1], [Oc2], [Po1], [Po2], [Po3], [Po4], [Wa], [We1], and [We2]). A particular approach suggests a particular kind of subfactor as the “simplest.” For instance, in Haagerup’s approach [H],...

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G . In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We ...