منابع مشابه
An extension of the Wedderburn-Artin Theorem
In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.
متن کاملA Morse-theoretical Proof of the Hartogs Extension Theorem
100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was understood later: holomorphic functions in a connected neighborhood V(∂Ω) of a connected boundary ∂Ω b C (n > 2) do extend holomorphically and uniquely to the domain Ω. Martinelli in the early 1940’s and Ehrenpreis in 1961 obtained a rigorous pro...
متن کاملHartogs Type Extension Theorems
Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...
متن کاملGeneralizing Hartogs’ Trichotomy Theorem
The Trichotomy Principle says that a pair of sets A and B either admits a bijection or else precisely one of these sets injects into the other. Hartogs established logical equivalence between the Trichotomy Principle and the Well-Ordering Principle. As ZF suffices to prove the Schröder-Bernstein theorem, the heart of Trichotomy lies in the existence of some injection connecting A and B (in eith...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1972-0296341-9