Authors: Bekkali, Mohamed
Todorčević, Stevo 
Title: Algebras that are hereditarily interval
Journal: Algebra Universalis
Volume: 73
Issue: 1
First page: 87
Last page: 95
Issue Date: 1-Jan-2014
Rank: M22
ISSN: 0002-5240
DOI: 10.1007/s00012-014-0315-y
Interval algebras are a class of Boolean algebras with a linearly ordered set of generators. This class of algebras is not hereditary, i.e., not closed under taking subalgebras. We investigate the problem of finding a natural subclass of this class that is hereditary. For example, we prove that s-centered subalgebras of interval algebras of size less than b are interval algebras themselves. We state a dual form of our result saying that continuous zero-dimensional images of ordered compacta of weight less than b are themselves ordered.
Keywords: cardinal b | interval algebras | ordered compacta | pseudotree algebras | zero-dimensional spaces | σ-centered algebras
Publisher: Springer Link

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