Inessentiality with respect to subspaces

Levin, Michael

Levin, Michael

Fundamenta Mathematicae, Tome 146 (1995), p. 93-68 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be a compactum and let $A = (A_{i}, B_{i}) : i = 1, 2, . . .$ be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed $F_{i}$ separating $A_{i}$ and $B_{i}$ the intersection $(\cap F_{i}) \cap Y$ is not empty. So A is inessential on Y if there exist closed $F_{i}$ separating $A_{i}$ and $B_{i}$ such that $\cap F_{i}$ does not intersect Y. Properties of inessentiality are studied and applied to prove: Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on which A is inessential and for every positive-dimensional Y ∩ X ╲ G there exists an infinite subfamily B ∩ A which is essential on Y. >This theorem and its generalization provide a new approach for constructing hereditarily infinite-dimensional compacta not containing subspaces of positive dimension which are weakly infinite-dimensional or C-spaces.

Publié le : 1995-01-01

Zbl 0868.54028

EUDML-ID : urn:eudml:doc:212077

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     author = {Michael Levin},
     title = {Inessentiality with respect to subspaces},
     journal = {Fundamenta Mathematicae},
     volume = {146},
     year = {1995},
     pages = {93-68},
     zbl = {0868.54028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv147i1p93bwm}
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Levin, Michael. Inessentiality with respect to subspaces. Fundamenta Mathematicae, Tome 146 (1995) pp. 93-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i1p93bwm/

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