On the Henstock Strong Variational Integral

1971 ◽  
Vol 14 (1) ◽  
pp. 87-99 ◽  
Author(s):  
B. S. Thomson
Keyword(s):  
Type Theory ◽  
Space Theory ◽  
Variational Integral ◽  
Locally Compact ◽  
New Approach ◽  
Simplified Approach ◽  
Compact Spaces ◽  
Locally Compact Spaces ◽  
Lebesgue Integration

The theory of integration in division spaces introduced by Henstock ([3], [4]) serves to unite and simplify much of the classical material on nonabsolute integration as well as to provide a new approach to Lebesgue integration. In this paper we sketch a simplified approach to the division space theory and show how it can lead rapidly to the standard Lebesgue-type theory without a substantial departure from the usual methods; some applications to integration in locally compact spaces are briefly developed.

On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces

2005 ◽  
Vol 57 (6) ◽  
pp. 1121-1138 ◽  
Author(s):  
Michael Barr ◽  
R. Raphael ◽  
R. G. Woods
Keyword(s):  
Locally Compact ◽  
Compact Spaces ◽  
Open Questions ◽  
Tychonoff Spaces ◽  
Locally Compact Spaces

AbstractWe study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.

About Weakly Locally Compact Spaces

2004 ◽  
pp. 638-644
Author(s):  
Tomas K. Breuckmann ◽  
Soraya R. T. Kudri ◽  
Halis Aygün
Keyword(s):  
Locally Compact ◽  
Compact Spaces ◽  
Locally Compact Spaces
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