scholarly journals Countably compact groups satisfying the open mapping theorem

1999 ◽  
Vol 98 (1-3) ◽  
pp. 81-129 ◽  
Author(s):  
Dikran Dikranjan
Keyword(s):  
Open Mapping ◽  
Compact Groups ◽  
Open Mapping Theorem ◽  
Countably Compact

Separating Singularities of Holomorphic Functions

1998 ◽  
Vol 41 (4) ◽  
pp. 473-477 ◽  
Author(s):  
Jürgen Müller ◽  
Jochen Wengenroth
Keyword(s):  
Approximation Theory ◽  
Classical Result ◽  
Short Proof ◽  
Holomorphic Functions ◽  
Open Mapping ◽  
Complex Approximation ◽  
Basic Tool ◽  
Open Mapping Theorem ◽  
Separation Results

AbstractWe present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for other classes of functions.

scholarly journals AN OPEN MAPPING THEOREM

2016 ◽  
Vol 94 (1) ◽  
pp. 65-69
Author(s):  
SAAK S. GABRIYELYAN ◽  
SIDNEY A. MORRIS
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Open Mapping ◽  
Locally Compact ◽  
Surjective Morphism ◽  
Open Mapping Theorem

It is proved that any surjective morphism $f:\mathbb{Z}^{{\it\kappa}}\rightarrow K$ onto a locally compact group $K$ is open for every cardinal ${\it\kappa}$. This answers a question posed by Hofmann and the second author.

scholarly journals Optimality of the quantified Ingham–Karamata theorem for operator semigroups with general resolvent growth

2019 ◽  
Vol 113 (6) ◽  
pp. 617-627 ◽  
Author(s):  
Gregory Debruyne ◽  
David Seifert
Keyword(s):  
Open Mapping ◽  
General Version ◽  
Operator Semigroups ◽  
Open Mapping Theorem ◽  
Mild Conditions ◽  
Technical Lemma ◽  
Resolvent Growth

Abstract We prove that a general version of the quantified Ingham–Karamata theorem for $$C_0$$C0-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty–Duyckaerts theorem is optimal even for bounded $$C_0$$C0-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a crucial technical lemma allowing us to strengthen our earlier results.

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