局部有限和仿紧空间的拟形理论
Quasi-shape theory of locally finite and paracompact spaces
摘要：
形理论对于（豪斯多夫）仿紧空间很适用，但是对于没有分离公理的空间，它似乎很差。然而，对于有限空间和局部有限空间，它们的弱同伦类型相当丰富，并且分别等价于有限和局部有限多面体的弱同伦类型。本文提出了一种变形的形理论，称为拟形，它既适用于仿紧空间，也适用于局部有限空间，即在局部有限空间中，拟形同构于弱同伦型，而在仿紧空间中，拟形与普通形是\natural -等价的。
英文摘要：
Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their weak homotopy type is rather rich, and is equivalent to the weak homotopy type of finite and locally finite polynedra, respectively. In the paper there is proposed a variant of shape theory called quasi-shape, which suits both paracompact and locally finite spaces, i.e. the quas-shape is isomorphic to the weak homotopy type for locally finite spaces, and is \natural-equivalent to the ordinary shape in the case of paracompact spaces.
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