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- W2949442920 abstract "A family $bfam$ of continuous real-valued functions on a space $X$ is said to be {sl basic} if every $f in C(X)$ can be represented $f = sum_{i=1}^n g_i circ phi_i$ for some $phi_i in bfam$ and $g_i in C(R)$ ($i=1, ..., n$). Define $basic (X) = min {|bfam| : bfam$ is a basic family for $X}$. If $X$ is separable metrizable $X$ then either $X$ is locally compact and finite dimensional, and $basic (X) < aleph_0$, or $basic (X) = mathfrak{c}$. If $K$ is compact and either $w(K)$ (the minimal size of a basis for $K$) has uncountable cofinality or $K$ has a discrete subset $D$ with $|D|=w(K)$ then either $K$ is finite dimensional, and $basic (K) = cof ([w(K)]^{aleph_0}, subseteq)$, or $basic (K) = |C(K)|=w(K)^{aleph_0}$." @default.
- W2949442920 created "2019-06-27" @default.
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- W2949442920 date "2009-09-24" @default.
- W2949442920 modified "2023-09-27" @default.
- W2949442920 title "Minimal Size of Basic Families" @default.
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