UN rules on asylum dating from 1951. They give every refugee the right to have an application for asylum at least considered by the country in which they apply.
The Convention does not settle any determination for the responsible State to examine an asylum application. That is why the Dublin Convention was signed to get common rules between the EU-countries.
The Lisbon Treaty now has a legal base for a common asylym policy decided by qualified majority in Art. 78 TFEU.