## Illinois Journal of Mathematics

- Illinois J. Math.
- Volume 22, Issue 3 (1978), 443-448.

### Locally analytically connected topologies

#### Abstract

We shall prove the existence of two natural analytic topologies which refine the given topology on a space with a specified collection of continuous complex-valued functions. Whereas one would expect [2] the two constructions always, to yield the same analytic refinement, we show by example that is not the case.

This work was motivated by the search for analytic structure in the maximal ideal space of a function algebra, in particular the existence of nontrivial holomorphic mappings of analytic varieties into the maximal ideal space. (For restrictions on what type of analytic varieties need be considered, see Section 4.)

#### Article information

**Source**

Illinois J. Math., Volume 22, Issue 3 (1978), 443-448.

**Dates**

First available in Project Euclid: 20 October 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.ijm/1256048606

**Digital Object Identifier**

doi:10.1215/ijm/1256048606

**Mathematical Reviews number (MathSciNet)**

MR497487

**Zentralblatt MATH identifier**

0469.46041

**Subjects**

Primary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]

Secondary: 46J20: Ideals, maximal ideals, boundaries 54C35: Function spaces [See also 46Exx, 58D15]

#### Citation

Wang, Helen P. Locally analytically connected topologies. Illinois J. Math. 22 (1978), no. 3, 443--448. doi:10.1215/ijm/1256048606. https://projecteuclid.org/euclid.ijm/1256048606