Generalized Open Mapping Theorem for X-Normed Spaces

2019 ◽  
Vol 11 (2) ◽  
pp. 135-150 ◽  
Author(s):  
Angel Barria Comicheo
Keyword(s):  
Open Mapping ◽  
Normed Spaces ◽  
Open Mapping Theorem

scholarly journals Fuzzy Open Mapping and Fuzzy Closed Graph Theorems in Fuzzy Length Space

2020 ◽  
Vol 25 (4) ◽  
pp. 32-39
Author(s):  
Raghad I. Sabri
Keyword(s):  
Linear Operator ◽  
Fuzzy Set ◽  
Open Mapping ◽  
Normed Spaces ◽  
Closed Graph ◽  
Closed Graph Theorem ◽  
Open Mapping Theorem ◽  
Length Space ◽  
Definition Of ◽  
First Time

The theory of fuzzy set includes many aspects that regard important and significant in different fields of science and engineering in addition to there applications. Fuzzy metric and fuzzy normed spaces are essential structures in the fuzzy set theory. The concept of fuzzy length space has been given analogously and the properties of this space are studied few years ago. In this work, the definition of a fuzzy open linear operator is presented for the first time and the fuzzy Barise theorem is established to prove the fuzzy open mapping theorem in a fuzzy length space. Finally, the definition of a fuzzy closed linear operator on fuzzy length space is introduced to prove the fuzzy closed graph theorem.    

scholarly journals Quotient operators and the open mapping theorem

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6221-6227
Author(s):  
Mahesh Krishna ◽  
Sam Johnson
Keyword(s):  
Open Mapping ◽  
Bounded Operators ◽  
Normed Spaces ◽  
Open Mapping Theorem

Quotients of bounded operators on normed spaces have been discussed. Openmapping theorem for quotients of bounded operators and its consequences are given.

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.

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