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Topology

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Topologies on Finite Sets II

TOPO-GNJXZ1

Consider the set $x=\{a,b,c\}$. Which of the following define topologies on $X$?

Select ALL that apply.

A

$\tau_1=\{\emptyset, X\}$

B

$\tau_2 = \{\emptyset, \{a\}, \{b\}, \{c\}, X\}$

C

$\tau_3 = \{\emptyset, \{a\}, \{a,b\}, \{a,c\}, X\}$

D

$\tau_4 = \{\{b\}, \{a,b\}, \{b,c\}, X\}$

E

$\tau_5 = \{\emptyset, \{b\}, \{c\}, \{a,c\}, \{b,c\}, X\}$