$\textbf{Topological space}$
A topological space is a set $X$ together with a collection of subsets $\tau$ of $X$ satisfying the following axioms:
1) The empty set and $X$ itself belong to $\tau$.
2) Any union (finite or infinite) of members of $\tau$ still belongs to $\tau$.
3) The intersection of any finite number of members of $\tau$ still belongs to $\tau$.
Note: The elements of $\tau$ are called open sets and the collection $\tau$ is called a topology on $X$.
$\textbf{Topological space}$
A topological space is a set $X$ together with a collection of subsets $\tau$ of $X$ satisfying the following axioms:
1) The empty set and $X$ itself belong to $\tau$.
2) Any union (finite or infinite) of members of $\tau$ still belongs to $\tau$.
3) The intersection of any finite number of members of $\tau$ still belongs to $\tau$.
Note: The elements of $\tau$ are called open sets and the collection $\tau$ is called a topology on $X$.
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𝐓𝐨𝐩𝐨𝐥𝐨𝐠𝐢𝐜𝐚𝐥 𝐬𝐩𝐚𝐜𝐞
A topological space is a set 𝑋 together with a collection of subsets 𝜏 of 𝑋 satisfying the following axioms:
1) The empty set and 𝑋 itself belong to 𝜏.
2) Any union (finite or infinite) of members of 𝜏 still belongs to 𝜏.
3) The intersection of any finite number of members of 𝜏 still belongs to 𝜏.
Note: The elements of 𝜏 are called open sets and the collection 𝜏 is called a topology on 𝑋.