Partitions of the Spectrum of a Topological Algebra through Geometric hulls

Από το τεύχος 44 του περιοδικού Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The aim of the present paper is to examine partitions of the spectrum mu(E) of a given topological algebra E, by means of suitable subsets of the spectrum by taking an appropriate covering of mu(E) and by considering the geometric hulls of its members. (The original result is given in Theorem 2.1). Furthermore according to author's approach the abovementioned decomposition of mu(E) may give a similar decomposition of the Gel'fand transform algebra of E by transforming it to a homeomorphism of the spaces involved within the addition of suitable conditions on the topological algebra, the spectrum and the initial covering. (The original results are given in Corollaries 2.1, 2.2). (This paper is based on a talk presented by the author in the 4th Panellenic Conference on Geometry on "Research in Geometry and in its Teaching towards the 21st century'' taking place in the University of Patras, Greece, 28--30 May 1999.)

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