**Generalised Inverse Limits**

## Department of Mathematics

# Generalised Inverse Limits

Inverse limits have been extensively studied by mathematicians for many years and have been widely applied through mathematics and in other fields such as economics and physics.

Generalised inverse limits (GILS) have only recently been introduced, and they are attracting a lot of interest. They involve subsets of infinite dimensional spaces whose coordinates are found by working backwards through (bonding) functions.

They differ from inverse limits in that the functions are set-valued functions so they are richer and can be more widely applied.

For example, we can create very complex continua by taking the generalised inverse limit with a single, simple bonding function.

We are interested in the relationship between the properties of inverse limits and the properties of their bonding functions.

Our current projects include indecomposability and dimension.

### Researchers at the University of Auckland

- Sina Greenwood
- Gareth Davies

- Michael Lockyer
- Bradley Windelborn

- Simon Youl

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**