Inessentiality with respect to subspaces

• Autorzy: Michael B. Levin
• Języki publikacji: EN

Abstrakty

EN

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 $(∩ F_i) ∩ Y $ is not empty. So A is inessential on Y if there exist closed $F_i$ separating $A_i$ and $B_i$ such that $∩ F_i$ 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.

Kategorie tematyczne

• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 1
• Strony: 93-68

Daty

wydano

1995

otrzymano

1994-08-29

Twórcy

autor

Michael B. Levin

• Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel

Bibliografia

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• [7] J. J. Walsh, Infinite dimensional compacta containing no n-dimensional (n ≥ 1) subsets, Topology 18 (1979), 91-95.