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The Suslinian number and other cardinal invariants of continua

T. Banakh;  V. V. Fedorchuk;  J. Nikiel;  M. Tuncali — 2010

Fundamenta Mathematicae

By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family ℂ of non-degenerate subcontinua of size |ℂ| > κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)⁺ and is the limit of an inverse well-ordered spectrum of length ≤ Sln(X)⁺, consisting of compacta with weight ≤ Sln(X) and...

Hereditarily indecomposable inverse limits of graphs

K. Kawamura;  H. M. Tuncali;  E. D. Tymchatyn — 2005

Fundamenta Mathematicae

We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map f ε : G → G which is ε-close to f such that the inverse limit ( G , f ε ) is hereditarily indecomposable.

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