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Homogeneous Convergence (等質収束) (Definition IV.10.14)

  • Homogeneous Convergence (等質収束) (Definition IV.10.14) #Card
    • A convergence $\xi$ is homogeneous if for every $x_0, x_1 \in |\xi|$ there exists $h \in H(\xi, \xi)$ such that $h(x_0) = x_1$.

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Section titled “Back”

A convergence $\xi$ is said to be homogeneous if for every $x_0, x_1 \in |\xi|$, there exists a self-homeomorphism $h \in H(\xi, \xi)$ such that $h(x_0) = x_1$（どの点も自己同相で他のどの点にも移せる）.

  • 等質な例: $\iota_X$, $o_X$, $\sigma_\mathbb{R}$, $\nu_\mathbb{R}$, 円周 $\rho$（Example IV.3.16）とその同相コピー $h\mu$。
  • 等質でない例: Sierpiński 前位相 $$_0, $_1$（孤立点と非孤立点は移り合えない）。