Mathematics to be formalized next
---------------------------------

This document lists the material that I would like to see added to IsarMathLib in the near future. It is intended as a suggestion for contributors.

1. Sequences defined recursively
    It is quite frequent in math that we define a sequence (that is, a function on natural numbers) by specifying the first element and a rule for creating new values from previous one(s). It would be nice to have an implementation of this in the ZF framework that does not use the word "datatype".

2. Algebraic topology
    We have topology, we have groups, let's have topological groups.

3. Metric spaces
    Let's start from defining a metric as a function with values in an ordered group with some desired properties, then see what is needed for different properties of metric spaces.

4. Real and complex analysis based on Metamath theorems 
    We are translating theorems from Metamath. One thing to do is to use the results from the translated part to make the library more complete. We should be careful here not to repeat theorems that are present in Metamath's set.mm database and will be translated later anyway.
5. Examples
    Real numbers allow to provide lots of examples of groups, rings, fields, topologies and metric spaces.

Modified 11/29/06