According to the eNotes summary on the EU (European Union), it is an alliance formed to "foster economic cooperation."Two countries have been denied admittance after having applied for EU membership. The first was Morocco because it was deemed to be outside the extent of a geographical Europe. Turkey, after many years of negotiating toward EU membership, was denied admittance in 2013 for reasons that included geographical extent of recognized Europe.
Curious about what countries would themselves decline an opportunity when invited to membership in the EU, I conducted a little research.
The EU-15 included Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, and the United Kingdom. EU-19 included the EU-15 plus Czech Republic, Hungary, Poland, and Slovak Republic.
There are at least five countries which have not applied or that have voted down membership when offered membership in the EU some are Switzerland, Andorra, Vatican City, Belarus, Russia, Kazakhstan, though some of these might also be considered outside the geographical extent of Europe.