FOM: Second Workshop on Formal Topology, Venice, April 2002

Giovanni Sambin sambin at
Wed Sep 12 13:24:17 EDT 2001


               Auditorium S. Margherita, Campo S. Margherita
                         Venice, April 4-6, 2002

organised by:
the EC Types Working Group
Dipartimento di Matematica Pura e Applicata, Universita' di Padova
Dipartimento di Informatica, Universita' Ca' Foscari, Venezia

This workshop is about a specific approach to formal, or pointfree, topology, which stresses its constructive features. Its historical roots include Brouwer's conception of the continuum, which was expressed in terms of choice sequences.  The later analysis and elimination of choice sequences led to connections with locale theory and inductive definitions, as in Martin-Loef's Notes on constructive mathematics.  So it aims at a theory of formal spaces, in some way similar to the present impredicative theory of locales, but expressed in a predicative constructive framework such as constructive type theory (Martin-Loef)  or constructive set theory (Aczel).

As time passed, the landscape of formal topology has become wider, and its distinctive predicative foundation has given rise to some unexpected mathematical developments (even the right approach to the notion of a `closed set' needs a conceptually new approach, where `closed' is not the complement of `open').  Nowadays it includes a variety of themes and novelties, which are of interest in:

- computer science, because of the methods of definition by induction and recently also by co-induction, the techniques for the extraction of constructive information from a priori non effective arguments and connections with domain theory, implementation problems, etc.;

- logic and foundations, because of the interaction between the foundations of mathematics and the actual development of mathematics, methods from proof theory in the practice of mathematics, sheaf models, the logical nature of topological definitions, etc.;

- mathematics itself, because of the process of constructivization - which often is accompanied by a conceptual simplification - of classical results of topology and of mathematics in general and also the connections with category theory and locale theory, etc..

The first workshop of this series took place in Padova, October 1997. It was widely appreciated for its relaxed and constructive atmosphere, and for an open discussion on various approaches.  Hopefully with a similar atmosphere, the aim of the second workshop will be to obtain an up-to-date picture of the foundational and technical issues concerning formal topology, and to clarify the connections with related approaches.

Invited speakers. The list of invited speakers at the moment includes Martin Escardo, Henri Lombardi, Peter Johnstone, Erik Palmgren, Mike Smyth, Steve Vickers.  

Tutorials.  The workshop will be preceeded by one day, 3 April 2002, of tutorials to help those people who are interested but have little or even no knowledge of formal topology.  At the moment, Peter Aczel and Giovanni Sambin have volunteered.

Contributed papers. Those who wish to contribute with  a half hour talk, should submit a summary of contents (from 1 to 10 pages) to Thierry Coquand, coquand at by 28 February 2002. The program committe will notify acceptance by 15 March 2002.

Proceedings. The proceedings will be published after the workshop, probably, a special issue of some good journal (hence with referees and open also to nonparticipants)

Registration. Registration is free; the form below must be sent to Giovanni Curi, gcuri at A convenient accomodation in Venice can be provided only to those participants who register by 30 September 2001. For a low cost accomodation (possibily in a common room), contact Claudia Faggian claudia at

Grants. We also plan to offer a limited number of grants for students and young researchers covering accomodation and food. Please send a short CV and motivations for participation to Giovanni Sambin sambin at

Site. Venice needs no presentation. But note that the site of the workshop is out of the main tourist routes, and should allow for an appreciation of the popular and historical aspects of the city. We expect to find convenient accomodations nearby.

Social Program. A trip will be organized for those who remain on Sunday 7 April 2002. An idea is to hire a boat and have lunch in an island of the lagoon. The full social program will be communicated later.

Second announcment. The second announcement will contain information updates and the web address of a page dedicated to the workshop (with details on place, accomodation, tourist information, trip, etc.).

The program committee

Peter Aczel
Thierry Coquand
Per Martin-Loef (chair)
Giovanni Sambin (local organization)
Dieter Spreen


September 30, 2001 : early registration (with safe accomodation)

February 28, 2002: deadline for the submission of papers

March 15, 2002: program is decided

April 3, 2002: tutorials

April 4 - 6, 2002:  workshop

April 7: trip for those who wish to remain, probably on a privately hired boat

Registration Form:

Name and Family name:
E-mail address:
Date of arrival:                  Date of departure:
Kind of accomodation (if required):
      low cost (common room, around 8 beds, price around 15 euros)          
      single room (Fondazione Levi or Palazzo Zenobio, price around 50 euros, maybe less)
      double-triple room (Fondazione Levi or Palazzo Zenobio, price around 35 euros)

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