(17 oct 2012: this post is obsolete since the second edition is now available from the same link below)

Recently published online, the book ‘Natural Topology’ finishes a project which Wim Couwenberg and I started already in 2004. See also my math page.

This blog is perhaps handy to post some addenda and corrections over the time to come, before creating a real revision as a second edition.

An important (but not difficult) addendum which I forgot to detail in the book itself:

**The composition of path morphisms**.

If are path morphisms from natural spaces to and to respectively, then how do we form the composition?

(where , , are derived from the pre-natural spaces , with (pre-natural) path spaces , )

The thing to notice is that is defined as a refinement morphism from to , but can be uniquely lifted to a refinement morphism from to .

This is straightforward, for a basic dot in , we put which is a basic dot in since is a refinement morphism.

We now define the composition of and to be the composition , which is a path morphism from to .

**The composition of a refinement morphism with a path morphism**.

Since any refinement morphism can be thought of as a path morphism (trivially), this has been dealt with above.

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## About fwaaldijk

mathematician (foundations & topology in constructive mathematics) and visual artist

A drawback to the term `path space’ only occurred to me recently, namely that this is also a term used in connection with usual topological spaces. The same applies a bit to the term `unglueing’. I will give some thought to finding other terms, for an ameliorated second edition.

Such second edition might also give a little more emphasis on the reason why we focus on refinement morphisms and spraids, which is elegance and computational efficiency mainly.