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Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

Paul Fabel — 1998

Fundamenta Mathematicae

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 to the separable Hilbert space $l_{2}$ .

Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)

Paul Fabel — 2011

Bulletin of the Polish Academy of Sciences. Mathematics

The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a naturally occuring example of a quotient map such that q × q fails to be a quotient map. With the quotient topology, this example shows π₁(X,p) can fail to be a topological group if X is locally path connected.

The topological Hawaiian earring group does not embed in the inverse limit of free groups.

Fabel, Paul — 2005

Algebraic & Geometric Topology

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Currently displaying 1 – 3 of 3

Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)

The topological Hawaiian earring group does not embed in the inverse limit of free groups.