## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 23, Issue 1 (2011), 12-18.

### A Continuous Bijection from $\ell^{2}$ Onto a Subset of $\ell^{2}$ Whose Inverse is Everywhere Unboundedly Discontinuous, with an Application to Packing of Balls in $\ell^2$

#### Abstract

There is a continuous bijection from $ \ell^{2}$ onto a subset of $\ell^{2}$ whose inverse is everywhere unboundedly discontinuous. If $B$ is a ball in $\ell^2$, then the continuous bijection defined on $\ell^2$ maps countably many mutually disjoint balls of $\ell^2$ into countably many mutually disjoint balls in $B$, making those images mutually disjoint.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 23, Issue 1 (2011), 12-18.

**Dates**

First available in Project Euclid: 1 August 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1312233179

**Digital Object Identifier**

doi:10.35834/mjms/1312233179

**Mathematical Reviews number (MathSciNet)**

MR2828729

**Zentralblatt MATH identifier**

1235.46031

**Subjects**

Primary: 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Secondary: 46B20: Geometry and structure of normed linear spaces

#### Citation

Creswell, Sam H. A Continuous Bijection from $\ell^{2}$ Onto a Subset of $\ell^{2}$ Whose Inverse is Everywhere Unboundedly Discontinuous, with an Application to Packing of Balls in $\ell^2$. Missouri J. Math. Sci. 23 (2011), no. 1, 12--18. doi:10.35834/mjms/1312233179. https://projecteuclid.org/euclid.mjms/1312233179