On characterization of absolutely continuous measures on locally compact spaces

1973 ◽  
Vol 77 (3) ◽  
pp. 206-210 ◽  
Author(s):  
Lawrence Gluck
Keyword(s):  
Locally Compact ◽  
Absolutely Continuous ◽  
Compact Spaces ◽  
Continuous Measures ◽  
Locally Compact Spaces ◽  
Absolutely Continuous Measures

scholarly journals On Hausdorff compactifications of non-locally compact spaces

1979 ◽  
Vol 2 (3) ◽  
pp. 481-486
Author(s):  
James Hatzenbuhler ◽  
Don A. Mattson
Keyword(s):  
Hausdorff Space ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Spaces ◽  
Hausdorff Compactifications ◽  
Set Of Points ◽  
Locally Compact Spaces

LetXbe a completely regular, Hausdorff space and letRbe the set of points inXwhich do not possess compact neighborhoods. AssumeRis compact. IfXhas a compactification with a countable remainder, then so does the quotientX/R, and a countable compactificatlon ofX/Rimplies one forX−R. A characterization of whenX/Rhas a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed.

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.

Absolutely Continuous Measures on Locally Compact Semigroups(1)

1975 ◽  
Vol 18 (1) ◽  
pp. 127-132 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Compact Semigroup ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Continuous Measures ◽  
Locally Compact Semigroups ◽  
Absolutely Continuous Measures

AbstractLet S be a locally compact Borel subsemigroup of a locally compact semigroup G. It is shown that the algebra of all "absolutely continuous' measures on S is isometrically order isomorphic to the algebra of all measures in M(G) which are "concentrated" and "absolutely continuous" on S.

scholarly journals Normality Versus Paracompactness in Locally Compact Spaces

2018 ◽  
Vol 70 (1) ◽  
pp. 74-96 ◽  
Author(s):  
Alan Dow ◽  
Franklin D. Tall
Keyword(s):  
Strong Form ◽  
Locally Compact ◽  
Compact Spaces ◽  
Correct Proof ◽  
Chang’S Conjecture ◽  
Collectionwise Hausdorff ◽  
Chang's Conjecture ◽  
Paracompact Spaces ◽  
Locally Compact Spaces

AbstractThis note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on ω1, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ω1.

A characterization of quotient algebras of Ll(G)

1969 ◽  
Vol 66 (3) ◽  
pp. 547-551 ◽  
Author(s):  
Donald E. Ramirez
Keyword(s):  
Continuous Functions ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Absolutely Continuous ◽  
Borel Measures ◽  
Bounded Functions ◽  
Continuous Measures ◽  
Stieltjes Transforms ◽  
Absolutely Continuous Measures

Let G be a locally compact Abelian group; Γ the dual group of G; C0(Γ) the algebra of continuous functions on Γ which vanish at infinity; CB(Γ) the continuous, bounded functions on Γ; M (G) the algebra of bounded Borel measures on G; L1(G) the algebra of absolutely continuous measures; and M(G)∩ the algebra of Fourier–Stieltjes transforms.

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.

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