Is it possible to construct a topology on every set?
Give an example of open set in $\mathbb{R}$ with usual topology, which is not an open interval.
Let $X=\{a\}$. Then what are the differences between discrete topology, indiscreet topology and confinite topology on $X$?
Let $X$ be a non-empty finite set. Then what is the difference between discrete and cofinite toplogy on $X$.
Let $\tau$ be a cofinite toplogy on $\mathbb{N}$. Then write any three element of $\tau$.
Let $(\mathbb{Z}, \tau)$ be a cofinite topological spaces.
Is $\mathbb{N}$ open in $\tau$?
Is $A=\{\pm 100,\pm 101, \pm 102, ... \}$ open in $\tau$?
Is $E=\{0,\pm 2,\pm 4,...\}$ open in $\tau$?
Is set of prime open in $\tau$?
Is $B=\{1,2,3,...,99\}$ closed in $\tau$?
Is $C=\{10^{10}+n : n \in \mathbb{Z} \}$ open in $\tau$?
Write the closure of the set $S=\left\{1+\frac{1}{n}: n \in \mathbb{N} \right\}$ in usual topology on $\mathbb{R}$.
What is the closure of the set $T=\{1,2,3,4,5 \}\cup (6,7) \cup (7,8] $ in usual topology on $\mathbb{R}$?
What is the closure of the set $U=\{101,102,103,...,200\}$ in a cofinite toplogy constructed on $\mathbb{Q}$?