JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Isomorphisms of $AC(\sigma )$ spaces

### Tom 228 / 2015

Studia Mathematica 228 (2015), 7-31 MSC: Primary 46J10; Secondary 46J35, 47B40, 26B30. DOI: 10.4064/sm228-1-3

#### Streszczenie

Analogues of the classical Banach–Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if $AC(\sigma _1)$ is algebra isomorphic to $AC(\sigma _2)$ then $\sigma _1$ is homeomorphic to $\sigma _2$. The converse however is false. In a positive direction we show that the converse implication does hold if the sets $\sigma _1$ and $\sigma _2$ are confined to a restricted collection of compact sets, such as the set of all simple polygons.

#### Autorzy

• Ian DoustSchool of Mathematics and Statistics
University of New South Wales
Sydney 2052 Australia
e-mail
• Michael LeinertInstitut für Angewandte Mathematik
Universität Heidelberg
Im Neuenheimer Feld 294
D-69120 Heidelberg, Germany
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek