Show continuous functions need not be open maps and open maps need not be continuous. A function from one metric space to another is said to be an open map
if it maps open sets to open sets. Similarly one can define a closed
map.

1-Provide a continuous function which does not map an open set to another open set?
2- Provide a function which maps every open set to another one but it is not a continuous function?


A) To violate openness you can give any map which is not bijective. 
B) Open maps which are not continuous
