The Baire property on the hyperspace of nontrivial convergent sequences

2020 ◽  
pp. 107505
Author(s):  
S. García-Ferreira ◽  
R. Rojas-Hernández ◽  
Y.F. Ortiz-Castillo
Keyword(s):  
Baire Property ◽  
Convergent Sequences

Some classes of ideal convergent sequences and generalized difference matrix operator

Filomat ◽  
2017 ◽  
Vol 31 (6) ◽  
pp. 1827-1834 ◽  
Author(s):  
S.A. Mohiuddine ◽  
B. Hazarika
Keyword(s):  
Matrix Operator ◽  
Difference Matrix ◽  
Convergent Sequences

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

On Lower and Semi-Lower Density Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 661-671
Author(s):  
Jacek Hejduk ◽  
Anna Loranty
Keyword(s):  
Density Operator ◽  
Baire Property ◽  
Density Operators ◽  
Dense Sets ◽  
Meager Sets ◽  
Algebras Of Sets

Abstract This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

The Subspace of Almost Convergent Sequences

2021 ◽  
Vol 62 (4) ◽  
pp. 616-620
Author(s):  
R. E. Zvolinskii ◽  
E. M. Semenov
Keyword(s):  
Convergent Sequences

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

2018 ◽  
Vol 39 (12) ◽  
pp. 1278-1290 ◽  
Author(s):  
Vakeel A. Khan ◽  
Kamal M. A. S. Alshlool ◽  
Sameera A. A. Abdullah
Keyword(s):  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Convergent Sequences

Matrix Transformations in an Incomplete Space

1968 ◽  
Vol 20 ◽  
pp. 727-734 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Linear Space ◽  
Cauchy Sequence ◽  
Convergent Sequence ◽  
Convergent Series ◽  
Matrix Transformations ◽  
Cauchy Sequences ◽  
Complex Linear ◽  
Incomplete Space ◽  
Bounded Sequences ◽  
Convergent Sequences

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

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