Def 17.1

̄𝑆={lim𝑘𝑥𝑘𝑥𝑘𝑆}𝑆
is closure of set 𝑆, it has following properties

  1. ̄𝑆 is closed
  2. ̄𝑆 is smallest closed set which contain set 𝑆

Def 18.1

𝑆 is dense in ̄𝑆
(𝑦̄𝑆)(𝑥𝑆)(𝜀>0)𝑑(𝑥,𝑦)<𝜀