The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a new and naturally occuring example of a quotient map such that q× q fails to be… (More)

The cockroach entomopoxvirus caused a chronic infection in cultures of the German cockroach Blattella germanica. Heavily infected specimens showed a reduced mobility. Ellipsoid virus occlusion bodies… (More)

The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify π 1 (HA) as a quotient of the Hawaiian earring… (More)

If an inverse limit space X = lim←Xn is constructed in similar fashion to the Hawaiian earring then π1(X) inherits a natural quotient topology from the space of loops in X, and the canonical… (More)

We exhibit aspherical spaces X and Y is whose fundamental groups, topologized in a natural way, are isomorphic but not homeomorphic. Consequently X and Y cannot have the same homotopy type.

Suppose a given space X can be realized as the inverse limit of nested retracts X n where X n admits a universal cover or X n has a certain more general property. In various ways this paper… (More)

A characterization of regular topological fundamental groups yields a ‘no retraction theorem’ for spaces constructed in similar fashion to the Hawaiian earring.

The fundamental group of a locally path connected metric space inherits the discrete topology in a natural way if and only if X is semilocally simply connected. We also provide a counterexample to a… (More)

∂U is locally connected and not a simple closed curve H induces a homeomorphism of the solid cylinder leaving invariant sufficiently many vertical lines to determine a rotation number. If ∂U is not… (More)

We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic… (More)