22 citations
7 papers
Universal Scaling in Mixing Correlated Growth with Randomness
A. Kolakowska, M. A. Novotny, P. S. Verma
We study two-component growth that mixes random deposition (RD) with a correlated growth process that occurs with probability p. We find that these composite systems are in the uni…
The Hawaiian earring group is topologically incomplete
Paul Fabel
The premier exhibition of the following phenomenon: The fundamental group of any Peano continuum constructed in similar fashion to the Hawaiian earring admits two natural distinct…
A characterization of spaces with discrete topological fundamental group
Paul Fabel
We offer a counterexample to a theorem in the literature and then repair the theorem as follows: The fundamental group of a locally path connected metric space inherits the discret…
A retraction theorem for topological fundamental groups with application to the Hawaiian earring
Paul Fabel
A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.
Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
Paul Fabel
We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundament…
A monomorphism theorem for the inverse limit of nested retracts
Paul Fabel
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the…