## 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*

- 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