# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Topologically Invertible Elements and Topological Spectrum

### Tom 54 / 2006

Bulletin Polish Acad. Sci. Math. 54 (2006), 257-271 MSC: Primary 46H05; Secondary 46H20. DOI: 10.4064/ba54-3-7

#### Streszczenie

Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x\mapsto x^{-1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

#### Autorzy

• Mati AbelInstitute of Pure Mathematics
University of Tartu
Liivi 2-614, 50409 Tartu, Estonia
e-mail
• Wiesław ŻelazkoInstitute of Mathematics