On vector lattices of continuous functions in locally compact spaces

1988 ◽  
Vol 52 (3-4) ◽  
pp. 227-232
Author(s):  
Duong Tan Thanh
Keyword(s):  
Continuous Functions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Vector Lattices ◽  
Locally Compact Spaces

scholarly journals THE KERNELS AND CONTINUITY IDEALS OF HOMOMORPHISMS FROM 𝒞0(Ω)

2010 ◽  
Vol 88 (1) ◽  
pp. 103-130 ◽  
Author(s):  
HUNG LE PHAM
Keyword(s):  
Banach Algebras ◽  
Continuous Functions ◽  
Prime Ideals ◽  
Locally Compact ◽  
Compact Spaces ◽  
Locally Compact Spaces

AbstractWe give a description of the continuity ideals and the kernels of homomorphisms from the algebras of continuous functions on locally compact spaces into Banach algebras. We also construct families of prime ideals satisfying a certain intriguing property in the algebras of continuous functions.

A Class of Function Algebras

1960 ◽  
Vol 12 ◽  
pp. 353-362 ◽  
Author(s):  
F. W. Anderson
Keyword(s):  
Continuous Functions ◽  
Regular Space ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Spaces ◽  
The Past ◽  
Function Algebras ◽  
Bounded Continuous Functions ◽  
Locally Compact Spaces

A problem which has generated considerable interest during the past couple of decades is that of characterizing abstractly systems of realvalued continuous functions with various algebraic or topological-algebraic structures. With few exceptions known characterizations are of systems of bounded continuous functions on compact or locally compact spaces. Only recently have characterizations been given of the systems C(X) of all realvalued continuous functions on an arbitrary completely regular space X (1). One of the main objects of this paper is to provide, by using certain special techniques, a characterization of C(X) for a particular class of (not necessarily compact) completely regular spaces.

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