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

100%

Fabel P.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

tom 59

nr 1

77-83

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.

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

100%

Fabel P.

Fundamenta Mathematicae

1998

tom 155

nr 3

201-214

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 $l_2$.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Fabel P.

1 2011

1 1998

Wyniki wyszukiwania

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

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