$\mathcal{P}(\mathbb{R})\text{'}$de topoloji

Question

$\mathbb{R}$ gerçel sayılar kümesi olmak üzere $\mathcal{P}(\mathbb{R})\text{'}$de $5,6$ ve $7$ elemanlı üç tane topoloji yazınız.

Answer 1

$\tau_5=\bigg\{\emptyset,\mathcal{P}(\mathbb{R}),\{(-\infty,0)\},\{(0,\infty)\},\{(-\infty,0),(0,\infty)\}\bigg\}\subset \mathcal{P}(\mathcal{P}(\mathbb{R}))$

$\tau_6=\bigg\{\emptyset,\mathcal{P}(\mathbb{R}),\{(-5,5)\},\{(-5,-1),(-5,5)\},\{(-2,2),(-5,5)\},\{(-5,-1),(-2,2),(-5,5)\}\bigg\}\subset \mathcal{P}(\mathcal{P}(\mathbb{R}))$

$\tau_7=\bigg\{\emptyset,\mathcal{P}(\mathbb{R}),\{(-5,5)\},\{(-2,2)\},\{(-5,-1),(-5,5)\},\{(-2,2),(-5,5)\},\{(-5,-1),(-2,2),(-5,5)\}\bigg\}\subset \mathcal{P}(\mathcal{P}(\mathbb{R}))$

Comments

Bazı yerlerde virgüller eksik ve $\{\}$ yerine $\emptyset$ yazarsan daha şık olur.

---

Düzenledim hocam, teşekkürler.