Can Scotland legally remain in the EU

The EU has informal programs for the "European regions" and Scotland is composed of 6 such regions. However, when it comes to the basic EU law, all of Scotland is just a somewhat random part of the U.K., currently an EU member state.

The EU obviously cannot separate Scotland from the U.K. in any way, as the status of Scotland is a purely internal affair of the U.K. Scotland couldn't remain in the EU without its recognized independence and statehood. It could only apply for a membership in the EU if it gained independence and was recognized by all member states of the EU as an independent country. But the admission process would have to start from scratch, just like for Serbia and other countries in the queue. Such an admission – which would also require the approval by all EU member states – is generally considered virtually impossible.

Even in the most favorable case in which Scotland became the only successor state of the U.K., and I don't really believe that anyone in England would allow such a thing, a new process of readmission would almost certainly have to begin.

Also, there's no way in which Scotland could become a part of the Eurozone. The Eurozone itself is widely considered a frozen project that won't expand for many years. The new member states must obey many conditions and even the counties that clearly obey all the material conditions such as my homeland of the Czech Republic are being told No. (Which is just a way to mask that the Czech Republic itself and other countries don't seem to have any desire to join the Eurozone these days.) However, it's plausible that Scotland could be allowed to use the Euro as a non-member, in the same way as Montenegro in former Yugoslavia.

Strategically, despite the higher support for the EU, the attempts of the hypothetical independent Scotland to join the EU could be dangerous for many reasons, especially if England and Wales weren't really supportive of the plan. Scotland would be divided from the rest of the EU by England. Many basic things could be rather complex and the influence of England would be huge, anyway.

People outside the U.K. shouldn't generally intervene into these affairs but if someone in Scotland expects that all the EU countries will actively work on the reincorporation of Scotland against the wishes of England and Wales, I am pretty certain that he is wrong. In the end, the support for the EU wasn't overwhelming even in Scotland. Whatever happens on the U.K. territory should be more or less approved by the main political institutions of the U.K. and its basic parts.