Natural Topology revised (second edition)

I’m happy to announce the second revised edition of `Natural Topology´, which is available online at:

In the second edition, we have rectified some omissions and minor errors from the first edition. Notably the composition of natural morphisms has now been properly detailed, as well as the definition of (in)finite-product spaces. The bibliography has been updated (but remains quite incomplete). We changed the names ‘path morphism’ and ‘path space’ to ‘trail morphism’ and ‘trail space’, because the term ‘path space’ already has a well-used meaning in general topology.

Also, we have strengthened the part of applied mathematics (the APPLIED perspective). We give more detailed representations of complete metric spaces, and show that natural morphisms are efficient and ubiquitous. We link the theory of star-finite metric developments to efficient computing with morphisms. We hope that this second edition thus provides a unified framework for a smooth transition from theoretical (constructive) topology to applied mathematics.


On this day it is 100 years ago that Brouwer delivered his inaugural address `Intuitionism and Formalism´ (14 October 1912). It seems fitting to post on this day, since the book can be seen as a big tribute to Brouwer’s topological mastership, which he used in building intuitionistic mathematics. Brouwer’s work has permeated throughout topology, constructive mathematics, computer science and foundations, yet the Netherlands seem wary to acknowledge his genius (compared for instance to the Turing commemoration this year…). 

Therefore, at least one mention from his own country on this special day seems appropriate.

Any and all comments have been and will be greatly appreciated.



About fwaaldijk

mathematician (foundations & topology in constructive mathematics) and visual artist
This entry was posted in Uncategorized. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s