Question Number 140407 by mnjuly1970 last updated on 07/May/21
$$\:\:\:\: \\ $$$$\:\:\:\:{prove}\:{that}\:\langle\:\mathrm{X}:=\mathbb{R}\:,\:\tau_{{e}} \:\rangle\:{is} \\ $$$$\:\:\:\:\:\:{a}\:{second}\:{topology}\:{space}\:. \\ $$$$\:\:\:\:\:\tau_{{e}} \:\:{is}\:\mathscr{E}{uclidian}\:{topology}\:{on}\:\mathbb{R}. \\ $$$$\:\:\:\mathrm{H}{int}\:::\:\:\mathcal{B}=\:\left\{\:\left({r}−\frac{\mathrm{1}}{{n}}\:,{r}+\frac{\mathrm{1}}{{n}}\right)\mid\:{r}\in\mathrm{Q}\:,\:{n}\in\mathbb{N}\right\} \\ $$$$\:\:\:{is}\:\:{a}\:{base}\:{for}\:\tau_{{e}\:} ….. \\ $$