## 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:
- February 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*

- 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*

- 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*

- 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

## 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

## 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