Positive Topology: A New Practice in Constructive Mathematics

— —

Giovanni Sambin (Professor of Mathematical Logic, Department of Mathematics, Professor of Mathematical Logic, Department of Mathematics, University of Padua, Italy)

Positive Topology

A New Practice in Constructive Mathematics

Giovanni Sambin (Professor of Mathematical Logic, Department of Mathematics, Professor of Mathematical Logic, Department of Mathematics, University of Padua, Italy)

$256.95

Hardback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Oxford University Press
29 August 2024

Philosophy: logic; Topology

Series: Oxford Logic Guides

Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline.

In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself.

The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.

By: Giovanni Sambin (Professor of Mathematical Logic Department of Mathematics Professor of Mathematical Logic Department of Mathematics University of Padua Italy)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm, Spine: 3mm
Weight: 5g
ISBN: 9780199232888
ISBN 10: 0199232881
Series: Oxford Logic Guides
Pages: 624
Publication Date: 29 August 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface About This Book 1: Dynamic Constructivism: A New Conception of Mathematics 2: The Minimalist Foundation: Basic Notions and Tools 3: Basic Pairs: Symmetry and Duality in Topology 4: Relation-Pairs: Continuity is a Commutative Square 5: Concrete Spaces: Benefits of Keeping a Base 6: Convergent Relation-Pairs: Towards Topology With Points 7: Basic Topologies: Pointfree Topology Without Convergence 8: Continuous Relations: Respecting Covers and Positivities 9: Positive Topologies and Formal Maps: Pointfree Topology 10: Ideal Spaces and Maps: Ideal Aspects Over Real Topology 11: Topological Systems: a Place for all Topological Notions 12: Overlap Algebras: the Power of a Set as an Algebra 13: Overlap Topologies: Putting Topology in Algebraic Terms Appendix A: Generating Positivity By Co-induction References Index

Giovanni Sambin has been doing research in logic and the foundations of mathematics since the 1970s. He is among the founders of provability logic and has been developing the field of topology since the 1990s, adopting a dynamic view in mathematical practice, leading to positive topology, a new, richer approach to constructive topology based on a dynamic vision of the nature of mathematics. He was the first president of the Italian Association of Logic and its Applications (AILA).