Missouri Journal of Mathematical Sciences

Uncountably Many Mutually Disjoint, Simply Connected, Contractible and Frechet Differentiable Subsets of the Sphere in $\ell^2$, Each of Which is Dense in the Sphere

Sam H. Creswell

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Abstract

Each sphere in $\ell^{2}$ contains uncountably many mutually disjoint, simply connected, Frechet differentiable and contractible subsets, each of which is dense in the sphere.

Article information

Source
Missouri J. Math. Sci., Volume 22, Issue 1 (2010), 3-9.

Dates
First available in Project Euclid: 1 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1312232715

Digital Object Identifier
doi:10.35834/mjms/1312232715

Mathematical Reviews number (MathSciNet)
MR2650056

Zentralblatt MATH identifier
1207.46016

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Citation

Creswell, Sam H. Uncountably Many Mutually Disjoint, Simply Connected, Contractible and Frechet Differentiable Subsets of the Sphere in $\ell^2$, Each of Which is Dense in the Sphere. Missouri J. Math. Sci. 22 (2010), no. 1, 3--9. doi:10.35834/mjms/1312232715. https://projecteuclid.org/euclid.mjms/1312232715


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References

  • S. H. Creswell, Uncountably many mutually disjoint, dense and convex subsets of $\ell^{2}$ with applications to path connected subsets of spheres, Missouri Journal of Mathematical Sciences, 21 (2009), 163–174.
  • T. W. Gamelin and R. E. Greene, Introduction to Topology, Saunders College Publishing, New York, 1983.
  • N. Young, An Introduction to Hilbert Space, Cambridge University Press, Cambridge, 1988.