Exchange rate and domestic money supply It seems an obvious fact (not explained by authors but stated) that when a Central Bank purchases foreign currency (to stabilise its own), the domestic money supply goes up. 

It seems to me that the CB in question would use its domestic currency to buy foreign exchange but I don't see how this increases domestic money supply (I assume domestic money supply to be the amount of domestic currency in circulation in the domestic market).
This question can be answered once a few facts are realized.


The Central Bank has a monopoly on the production of currency;
The Central Bank can purchase foreign currency by using currency it has either already produced but stored in its vault or by producing new units of the currency;
The currency that the Central Bank has produced but stored in its vault or not produced yet are not in circulation;
By purchasing foreign currency the Central Bank brings its currency in circulation;
This currency can be brought out of circulation by the Central Bank purchasing this currency with assets such as foreign currency and destroying it afterwards or by anyone else doing exactly the same. 


If we therefore define the domestic money supply as the currency in circulation, then purchases by the Central Bank of foreign currency will bring currency in circulation from either its vault or its press.