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تسجيل مستخدم جديدThe Suslinian number and other cardinal invariants of continua
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By the {em Suslinian number} $Sln(X)$ of a continuum $X$ we understand the smallest cardinal number $kappa$ such that $X$ contains no disjoint family $C$ of non-degenerate subcontinua of size $|C|gekappa$. 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 $leSln(X)^+$ and is the limit of an inverse well-ordered spectrum of length $le Sln(X)^+$, consisting of compacta with weight $leSln(X)$ and monotone bonding maps. Moreover, $w(X)leSln(X)$ if no $Sln(X)^+$-Suslin tree exists. This implies that under the Suslin Hypothesis all Suslinian continua are metrizable, which answers a question of cite{DNTTT1}. On the other hand, the negation of the Suslin Hypothesis is equivalent to the existence of a hereditarily separable non-metrizable Suslinian continuum. If $X$ is a continuum with $Sln(X)<2^{aleph_0}$, then $X$ is 1-dimensional, has rim-weight $leSln(X)$ and weight $w(X)geSln(X)$. Our main tool is the inequality $w(X)leSln(X)cdot w(f(X))$ holding for any light map $f:Xto Y$.
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