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 | Abstract: | 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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