skeletal maps
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2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Andrzej Kucharski ◽  
Szymon Plewik ◽  
Vesko Valov

AbstractWe introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)] consisting of skeletal maps.


2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Taras Banakh ◽  
Andrzej Kucharski ◽  
Marta Martynenko

AbstractWe prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.


2012 ◽  
Vol 159 (10-11) ◽  
pp. 2679-2693
Author(s):  
Taras Banakh ◽  
Andrzej Kucharski ◽  
Marta Martynenko
Keyword(s):  

2011 ◽  
Vol 61 (3) ◽  
Author(s):  
Ricardo Carrera

AbstractW∞ denotes the category of archimedean ℓ-groups with designated weak unit and complete ℓ-homomorphisms that preserve the weak unit. CmpT2,∞ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on W∞ and its dual a functorial covering function on CmpT2,∞.We demonstrate that functorial polar functions give rise to reflective hull classes in W ∞ and that functorial covering functions give rise to coreflective covering classes in CmpT 2,∞. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal α, the class of α-projectable ℓ-groups is reflective in W ∞, and the class of α-disconnected compact Hausdorff spaces is coreflective in CmpT 2,∞. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).


2008 ◽  
Vol 17 (5) ◽  
pp. 467-486 ◽  
Author(s):  
Jorge Martínez ◽  
Eric R. Zenk
Keyword(s):  

2007 ◽  
Vol 16 (4) ◽  
pp. 521-533 ◽  
Author(s):  
Jorge Martínez ◽  
Eric R. Zenk
Keyword(s):  

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