scholarly journals Some examples of continuous images of Radon-Nikodým compact spaces

2009 ◽  
Vol 59 (4) ◽  
pp. 1027-1038 ◽  
Author(s):  
Alexander D. Arvanitakis ◽  
Antonio Avilés
Keyword(s):  
Compact Spaces ◽  
Continuous Images

Continuous Images of Compact Semilattices

1987 ◽  
Vol 30 (1) ◽  
pp. 109-113 ◽  
Author(s):  
Murray Bell ◽  
Jan Pelant
Keyword(s):  
Compact Space ◽  
Infinite Cardinal ◽  
Theoretic Property ◽  
Compact Spaces ◽  
General Order ◽  
Isolated Point ◽  
Continuous Images

AbstractHyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.

scholarly journals On two problems concerning Eberlein compacta

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Witold Marciszewski
Keyword(s):  
Banach Spaces ◽  
Compact Space ◽  
Dimensional Subspace ◽  
Weakly Compact ◽  
Compact Spaces ◽  
Eberlein Compact ◽  
Continuous Images

AbstractWe discuss two problems concerning the class Eberlein compacta, i.e., weakly compact subspaces of Banach spaces. The first one deals with preservation of some classes of scattered Eberlein compacta under continuous images. The second one concerns the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. We show that the existence of such Eberlein compacta is consistent with . We also show that it is consistent with that each Eberlein compact space of weight $$> \omega _1$$ > ω 1 contains a nonmetrizable closed zero-dimensional subspace.

scholarly journals Maximal pseudocompact spaces and the Preiss-Simon property

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Ofelia Alas ◽  
Vladimir Tkachuk ◽  
Richard Wilson
Keyword(s):  
Compact Space ◽  
Compact Spaces ◽  
Pseudocompact Space ◽  
Pseudocompact Spaces ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Continuous Images

AbstractWe study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under continuous images while this is not true for the class of countably compact spaces. We prove that every Fréchet-Urysohn compact space is homeomorphic to a retract of a compact MP-space. We also give a ZFC example of a Fréchet-Urysohn compact space which is not maximal pseudocompact. Therefore maximal pseudocompactness is not preserved by continuous images in the class of compact spaces.

Universal spaces for classes of scattered eberlein compact spaces

2006 ◽  
Vol 71 (3) ◽  
pp. 1073-1080 ◽  
Author(s):  
Murray Bell ◽  
Witold Marciszewski
Keyword(s):  
Compact Spaces ◽  
Universal Space ◽  
Uncountable Cardinal ◽  
Universal Element ◽  
Eberlein Compact ◽  
Universal Spaces ◽  
Continuous Images

AbstractWe discuss the existence of universal spaces (either in the sense of embeddings or continuous images) for some classes of scattered Eberlein compacta. Given a cardinal κ, we consider the class δκof all scattered Eberlein compact spaces K of weight ≤ κ and such that the second Cantor-Bendixson derivative of K is a singleton. We prove that if κ is an uncountable cardinal such that κ = 2≤κ, then there exists a space X in δκ such that every member of δκ is homeomorphic to a retract of X. We show that it is consistent that there does not exist a universal space (either by embeddings or by mappings onto) in . Assuming that = ω1, we prove that there exists a space X ∈ which is universal in the sense of embeddings. We also show that it is consistent that there exists a space X bΕ, universal in the sense of embeddings, but δω1 does not contain an universal element in the sense of mappings onto.

On Simply* Compact Spaces

2019 ◽  
Vol 26 (4) ◽  
pp. 196-200
Keyword(s):  
Compact Spaces

On Simply* Compact Spaces

2019 ◽  
Vol 264 (1) ◽  
pp. 196-200
Keyword(s):  
Compact Spaces
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