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Structural Crystallography of Inorganic Oxysalts

Sergey V. Krivovichev

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199213207
eISBN:
9780191707117
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213207.001.1
Subject:
Physics, Crystallography

This book deals with the structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and the methods of its description. The latter include ... More


PREDICATIVE EXPONENTIATION OF LOCALLY COMPACT FORMAL TOPOLOGIES OVER INDUCTIVELY GENERATED TOPOLOGIES

Maria Emilia Maietti

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0013
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Martin Hyland first classified the exponentiable locales as the locally compact ones. This chapter proves the counterpart of Hyland's result for inductively generated formal topologies. More ... More


Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper ... More


From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Laura Crosilla and Peter Schuster (eds)

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Constructive mathematics is a vital area of research which has gained special attention in recent years due to the distinctive presence of computational content in its theorems. This characteristic ... More


Links as Sasakian Manifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0010
Subject:
Mathematics, Geometry / Topology

This chapter is devoted to the geometry of links of isolated hypersurface singularities, as well as a review of the differential topology of homotopy spheres a la Kervaire and Milnor. The ... More


Topology

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0006
Subject:
Economics and Finance, Econometrics

This chapter discusses topological spaces and associated concepts, including first‐ and second‐countability, compactness, and separation properties. Weak topologies are defined. The case of product ... More


THE NONPARAMETRIC RADON TRANSFORM

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0002
Subject:
Mathematics, Mathematical Physics

This chapter focuses on the nonparametric Radon transform in detail. In particular, it derives the surjectivity and the range conditions, and describes the topology of the image of the Radon ... More


SEPARATION PROPERTIES IN CONSTRUCTIVE TOPOLOGY

Peter Aczel and Christopher Fox

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0011
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies separation properties in topology as done on the basis of the formal system CZF. Until the 1970s, there was only a limited focus on the general notion of a topological space in ... More


SPACES AS COMONOIDS

A. Bucalo and G. Rosolini

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0012
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The constructive approach to topology has produced a wealth of new insights about spaces, almost reaching the point of making these more elementary than sets. In particular, the point of view taken ... More


SOME CONSTRUCTIVE ROADS TO TYCHONOFF

Steven Vickers

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0014
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses the Tychonoff Theorem with respect to point-free topology from the point of view of both topos-valid and predicative mathematics. A new proof of the infinitary Tychonoff ... More


THE CONSTRUCTIVE UNIQUENESS OF THE LOCALLY CONVEX TOPOLOGY ON ℝ N

Douglas Bridges and Luminita Vîtă

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0020
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proves constructively that every n-dimensional real locally convex space is homeomorphic to ℝn. Although essentially nonconstructive theorems of real analysis are used in the customary ... More


INTRODUCTION

Laura Crosilla and Peter Schuster

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This introductory chapter sets the stage for the following chapters. It first discusses the issue of foundational systems for constructive mathematical practice, and expresses the desire for a closer ... More


INTEGRAL PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter deals with integral problems. Using examples, it illustrates the need to use weak topologies to obtain compactness and coerciveness conditions. The sufficiency and necessity of the ... More


Modeling food-web dynamics: complexity–stability implications

Jennifer A. Dunne, Ulrich Brose, Richard J. Williams, and Neo D. Martinez

in Aquatic Food Webs: An ecosystem approach

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198564836
eISBN:
9780191713828
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564836.003.0011
Subject:
Biology, Aquatic Biology

One of the challenges in the study of complex systems is how to integrate recent network structure discoveries with advances in modeling the dynamics of large non-linear systems. This is important ... More


The topology of ecological interaction networks: the state of the art

Owen L. Petchey, Peter J. Morin, and Han Olff

in Community Ecology: Processes, Models, and Applications

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199228973
eISBN:
9780191711169
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228973.003.0002
Subject:
Biology, Ecology

This chapter considers topology, i.e. the shape and structure of networks of interacting organisms in ecological systems. Species often form the nodes of such networks, though life stages, age ... More


The Shape of Space I: Topology

Nick Huggett

in Everywhere and Everywhen: Adventures in Physics and Philosophy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780195379518
eISBN:
9780199776559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379518.003.0004
Subject:
Philosophy, Philosophy of Science

The question of the ‘shape’ of space can be approached in two ways: whether space is ‘curved’ or ‘flat’ is discussed later, these chapters address ‘topology’, the properties that would stay the same ... More


Beyond the Third Dimension?

Nick Huggett

in Everywhere and Everywhen: Adventures in Physics and Philosophy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780195379518
eISBN:
9780199776559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379518.003.0005
Subject:
Philosophy, Philosophy of Science

The question of the ‘shape’ of space can be approached in two ways: whether space is ‘curved’ or ‘flat’ is discussed later, these chapters address ‘topology’, the properties that would stay the same ... More


Why Three Dimensions?

Nick Huggett

in Everywhere and Everywhen: Adventures in Physics and Philosophy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780195379518
eISBN:
9780199776559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379518.003.0006
Subject:
Philosophy, Philosophy of Science

The question of the ‘shape’ of space can be approached in two ways: whether space is ‘curved’ or ‘flat’ is discussed later, these chapters address ‘topology’, the properties that would stay the same ... More


Village, Empire, Desert

Stephen Clingman

in The Grammar of Identity: Transnational Fiction and the Nature of the Boundary

Published in print:
2009
Published Online:
January 2009
ISBN:
9780199278497
eISBN:
9780191706981
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278497.003.0007
Subject:
Literature, 20th-century and Contemporary Literature

South Africa under apartheid presented some of the issues of this book in concentrated form: whether it was possible to construct an alternative grammar of identity; whether a closed system could be ... More


The Aharonov–Bohm effect

Richard Healey

in Gauging What's Real: The Conceptual Foundations of Gauge Theories

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199287963
eISBN:
9780191713453
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287963.003.0002
Subject:
Philosophy, Philosophy of Science

This chapter introduces the Aharonov-Bohm effect and explains why it poses a challenge to classical conceptions of how electricity and magnetism act on charged particles. It offers a critical ... More


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