TITLE: Let $X$ be any set $\tau : = \{X-\{a_1 , a_2 ,......, a_n\} \cup \phi\}$. Is $(X , \tau )$ $T_1$?
QUESTION [2 upvotes]: I can not understand the topology $\tau$. Can anyone please help me to understand?

REPLY [1 votes]: The topology that is meant is most likely:
$$\tau = \{X\setminus F\mid F\subseteq X\text{ finite }\} \cup \{\emptyset\}$$
And a topology on $X$ is $T_1$ iff for all $x \in X$, $\{x\}$ is closed. Now decide... Whether $X$ is a $T_2$ space will depend on the size of $X$..
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