hewitt realcompactification
Recently Published Documents


TOTAL DOCUMENTS

9
(FIVE YEARS 0)

H-INDEX

4
(FIVE YEARS 0)

2020 ◽  
Vol 44 (6) ◽  
pp. 2330-2336
Author(s):  
Sadık EYİDOĞAN ◽  
Mehmet ONAT

2019 ◽  
Vol 69 (2) ◽  
pp. 469-473 ◽  
Author(s):  
Mehrdad Namdari ◽  
Mohammad Ali Siavoshi

Abstract It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are C-embedded. In particular, this generalizes the well-known fact that every countable subset of P-spaces are C-embedded. In the presence of the measurable cardinals, we observe that if X is a discrete space then every subspace of υ X (i.e., the Hewitt realcompactification of X) whose cardinal is nonmeasurable, is a C-embedded, discrete realcompact subspace of υ X. This generalizes the well-known fact that the discrete spaces with nonmeasurable cardinal are realcompact.


2003 ◽  
Vol 26 (3) ◽  
pp. 363-373
Author(s):  
S. K. Acharyya ◽  
K. C. Chattopadhyay ◽  
G. G. Ray

1995 ◽  
Vol 2 (1) ◽  
pp. 47-58 ◽  
Author(s):  
S. K. Acharyya ◽  
K. C. Chattopadhyay ◽  
G. G. Ray

1975 ◽  
Vol 20 (3) ◽  
pp. 359-365 ◽  
Author(s):  
A. Sultan

Several authors have studied various types of rings of continuous functions on Tychonoff spaces and have used them to study various types of compactifications (See for example Hager (1969), Isbell (1958), Mrowka (1973), Steiner and Steiner (1970)). However many important results and properties pertaining the Stone-Čech compactification and the Hewitt realcompactification can be extended to a more general setting by considering appropriate lattices of sets, generalizing that of the lattice of zero sets in a Tychonoff space. This program was first considered by Wallman (1938) and Alexandroff (1940) and has more recently appeared in Alo and Shapiro (1970), Banachewski (1962), Brooks (1967), Frolik (1972), Sultan (to appear) and others.


1975 ◽  
Vol 5 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Robert L. Blair ◽  
Anthony W. Hager

1970 ◽  
Vol 22 (3) ◽  
pp. 645-656 ◽  
Author(s):  
William G. McArthur

The Hewitt realcompactification vX of a completely regular Hausdorff space X has been widely investigated since its introduction by Hewitt [17]. An important open question in the theory concerns when the equality v(X × Y) = vX × vY is valid. Glicksberg [10] settled the analogous question in the parallel theory of Stone-Čech compactifications: for infinite spaces X and Y, β(X × Y) = βX × β Y if and only if the product X × Y is pseudocompact. Work of others, notably Comfort [3; 4] and Hager [13], makes it seem likely that Glicksberg's theorem has no equally specific analogue for v(X × Y) = vX × vY. In the absence of such a general result, particular instances may tend to be attacked by ad hoc techniques resulting in much duplication of effort.


Sign in / Sign up

Export Citation Format

Share Document