[FOM] Natural Topology revised edition (and 100 years since `Intuitionism and Formalism´)

frank waaldijk fwaaldijk at gmail.com
Sun Oct 14 17:51:04 EDT 2012

Dear all,

A second revised edition of the book `Natural Topology´ is now available
online from my website at:


An abstract of the first edition was given on FoM in

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.

I will be looking to put the book on arXiv in the coming month or so. But
today is the 100th birthday of Brouwer`s inaugural address `Intuitionism
and Formalism<http://www.ams.org/journals/bull/1913-20-02/S0002-9904-1913-02440-6/S0002-9904-1913-02440-6.pdf>´
(delivered 14 October 1912 at the University of Amsterdam), so it seems
fitting to post this today on FoM.

This 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 on the book have been and will be greatly appreciated!

Kind regards,

Frank Waaldijk
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