Nakahara §2.4.1 所讨论的研究空间及其连续变形下分类的学科；不是某集合上的开集族（拓扑结构）。该段是学科用途说明，未冒充形式定义。
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Nakahara · second-edition-local · §2.4.1 · PDF 第104页
As we mentioned at the beginning of this chapter, the main purpose of topology
is to classify spaces. Suppose we have several figures and ask ourselves which
are equal and which are different. Since we have not defined what is meant by
equal or different, we may say ‘they are all different from each other’ or ‘they
are all the same figures’. Some of the definitions of equivalence are too stringent
and some are too loose to produce any sensible classification of the figures or
spaces. For example, in elementary geometry, the equivalence of figures is given
by congruence, which turns out to be too stringent for our purpose. In topology,
we define two figures to be equivalent if it is possible to deform one figure into the
other by continuous deformation. Namely we introduce the equivalence relation
under which geometrical objects are classified according to whether it is possible
to deform one object into the other by continuous deformation. To be more
mathematical, we need to introduce the following notion of homeomorphism.原书定义条件与符号保留在引文中；不推断跨书等价。
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- href=“02-section-2-2.md#bound-definition-a8be1cd876f139cee42d0c2d”
- href=“01-section-2-1.md#bound-definition-c624ec2b869cd03c185835db”
- href=”../chapter-02/03-section-2-3.md#bound-definition-bea63120260758e422dc7e27”
- href=”../chapter-08/05-section-8-5.md#bound-definition-286572dc695bf2abe6f8eac1”
- href=”../chapter-05/index.md#bound-definition-2d833ac0bb979a1a384519d5”