# Norming infinitesimals of large fields

@inproceedings{Dales2017NormingIO, title={Norming infinitesimals of large fields}, author={H. Garth Dales}, year={2017} }

We give a survey of results on norming the infinitesimals of large fields and on constructing discontinuous homomorphisms from Banach algebras of continuous functions; we raise questions that remain from earlier work. The article is expanded from a talk given in Harvard on 27 March 2015 at the conference in honour of the 60th birthday of W. Hugh Woodin. It includes some historical remarks about the first written mathematics of Hugh.

## 2 Citations

### Set theory and the analyst

- PsychologyEuropean Journal of Mathematics
- 2018

This survey is motivated by specific questions arising in the similarities and contrasts between (Baire) category and (Lebesgue) measure—category-measure duality and non-duality, as it were. The bulk…

### ICLE Set theory and the analyst

- Psychology
- 2018

This survey is motivated by specific questions arising in the similarities and contrasts between (Baire) category and (Lebesgue) measure—category-measure duality and non-duality, as it were. The bulk…

## References

SHOWING 1-10 OF 32 REFERENCES

### Universal properties of some commutative radical Banach algebras.

- Mathematics
- 1981

Let K be any infinite compact space, and let V (K) be the algebra of all continuous complex-valued functions over K. Using the continuum hypothesis G. Dales and the author have constmcted…

### Homomorphisms of Commutative Banach Algebras

- Mathematics
- 1960

If v: f -> 3, then the function I = I v(x) 11, x C W, is a multiplicative semi-norm on W. Conversely (cf. Section 1), every multiplicative semi-norm is the norm of a homomorphism. Thus all our…

### Homomorphisms of C -Algebras

- Mathematics
- 2012

In this note we give a straightforward proof of the fact that every continuous homomorphism from a C ∗ -algebra into a weakly sequential complete Banach algebra is a finite rank operator. We also…

### Introduction to Banach Spaces and Algebras

- Mathematics
- 2010

PART I INTRODUCTION TO BANACH SPACES 1. Preliminaries 2. Elements of normed spaces 3. Banach spaces PART II BANACH ALGEBRAS 4. Banach algebras 5. Representation theory 6. Algebras with an involution…

### Discontinuous homomorphisms from C(K)

- Mathematics
- 1982

The conjecture that every algebra norm || • || on C(X) is equivalent to the uniform norm arises naturally from a theorem of Kaplansky in 1949 that necessarily 11/11 > \f\x ( ƒ e C(X)): see [9, 10.1].…

### Banach algebras and automatic continuity

- Mathematics
- 2000

Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras,…

### Super-Real Fields: Totally Ordered Fields with Additional Structure

- Mathematics
- 1996

Introduction 1. Ordered sets and ordered groups 2. Ordered fields 3. Completions of ordered groups and fields 4. Algebras of continuous functions 5. Normability and universality 6. The operational…

### The Theory of Ultrafilters

- Mathematics
- 1974

1. Set Theory.- Ordinals.- Cardinal Arithmetic.- Notes for 1.- 2. Topology and Boolean Algebras.- Topology.- Finitary Properties of Boolean Algebras.- Stone's Duality.- The Completion of a Boolean…

### Iterated Cohen extensions and Souslin's problem*

- Mathematics
- 1971

We can characterize the real line, up to order isomorphism, by the following list of properties: R is order complete, order dense, has no first or last elements, and contains a countable dense…