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Stegall compact spaces which are not fragmentable

✍ Scribed by Ondřej Kalenda

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
122 KB
Volume
96
Category
Article
ISSN
0166-8641

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✦ Synopsis

Using modifications of the well-known construction of "double-arrow" space we give consistent examples of nonfragmentable compact Hausdorff spaces which belong to Stegall's class S. Namely the following is proved.

(1) If ℵ 1 is less than the least inaccessible cardinal in L and MA & ¬CH hold then there is a nonfragmentable compact Hausdorff space K such that every minimal usco mapping of a Baire space into K is singlevalued at points of a residual set.

(2) If V = L then there is a nonfragmentable compact Hausdorff space K such that every minimal usco mapping of a completely regular Baire space into K is singlevalued at points of a residual set.

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