Abstract We consider generalized inverse limits of continua with bonding functions F n that have the projection of Graph( F n ) onto the second (first) factor atomic and images (pre-image) of points are zero-dimensional. For such bonding functions we show that under some easily verified conditions that if the first (all) factor space(s) has a certain property then the inverse limit space must have this property. The properties considered include; hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. We illustrate the theorems by several examples.

中文翻译：

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逆极限和原子投影

摘要 我们考虑具有键合函数 F n 的连续体的广义逆极限，其具有 Graph( F n ) 到第二（第一）因子原子的投影，并且点的图像（原像）是零维的。对于这样的结合函数，我们表明在一些容易验证的条件下，如果第一个（所有）因子空间具有某个属性，那么逆极限空间必须具有这个属性。考虑的属性包括：遗传可分解性、遗传不可分解性、遗传单相干性、弧形和树形。我们通过几个例子来说明定理。