scholarly journals Bitopological local compactness

1972 ◽  
Vol 75 (5) ◽  
pp. 407-411 ◽  
Author(s):  
Ivan L Reilly
Keyword(s):  
Local Compactness

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

scholarly journals Locally compact semi-algebras generated by a commuting operator family

1994 ◽  
Vol 17 (4) ◽  
pp. 717-724
Author(s):  
N. R. Nandakumar ◽  
Cornelis V. Vandermee
Keyword(s):  
Spectral Properties ◽  
Linear Operators ◽  
Finite Collection ◽  
Operator Family ◽  
Locally Compact ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Compactness

Conditions are provided for the local compactness of the closed semi-algebra generated by a finite collection of commuting bounded linear operators with equibounded iterates in terms of their joint spectral properties.

Domains of Paracompactness and Local Compactness

1976 ◽  
Vol 28 (3) ◽  
pp. 449-454
Author(s):  
Brian Warrack
Keyword(s):  
Topological Spaces ◽  
Local Compactness

Given a class of topological spaces and a class of mappings of topological spaces, the -résolvant of is denned to be the class of topological spaces all of whose -images lie in . Whenever is closed under composition and includes identity maps, is easily seen to be the largest class of spaces smaller than which is closed under -images.

scholarly journals Topological Dual Systems for Spaces of Vector Measurep-Integrable Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
P. Rueda ◽  
E. A. Sánchez Pérez
Keyword(s):  
Type Theorem ◽  
Classical Case ◽  
Function Spaces ◽  
Dual Systems ◽  
Banach Function Spaces ◽  
Infinite Dimensional ◽  
Local Compactness ◽  
Finite Dimensional ◽  
Integrable Functions ◽  
Vector Valued

We show a Dvoretzky-Rogers type theorem for the adapted version of theq-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector valued version of convergence in the weak topology, is equivalent to the convergence with respect to the norm. Examples and applications are also given.

Compact boundedness in periodic functional differential equations with infinite delay

1990 ◽  
Vol 114 (3-4) ◽  
pp. 291-297
Author(s):  
Junji Kato
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Periodic Systems ◽  
Compact Set ◽  
Ultimate Boundedness ◽  
Local Compactness ◽  
Non Local ◽  
Functional Differential

SynopsisIt is the aim of this article to consider some problems arising from the non local-compactness of the phase space for functional differential equations. The compact boundedness, that is, the boundedness depending on each compact set involving the initial values, is proved to be implied from the ultimate boundedness for periodic systems of functional differential equations on Cγ: = {φ ∊ C((–∞,0]) Note that it is known that the compactness cannot be dropped in the above. An example is also given to show that the asymptotic stability is not necessarily uniform even for periodic functional differential equations on Co.

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