Topologija (FMF)/Naloge/Izpit-2006-06-19/Naloga4

Iz MaFiRaWiki

Naj bo

  • X_1 = \mathbb{R}^2,
  • Y_1 = \{x \in \mathbb{R} \mid 1 \leq |x|\} \times \mathbb{R},
  • X_2 = \{(x, y) \in \mathbb{R}^2 \mid 1 < x^2 + y^2 < 4\} in
  • Y_2 = (1, 2) \times \{0\}.

Pokaži, da sta kvocientna prostora X1 / Y1 in X2 / Y2 homeomorfna.

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