Sorry not relevant to the subject, but who is allowed to trade after-hours? How come some people are allowed to take advantage of trading while the general public is not allowed?
This is different from options or margin trading, where only registered accounts can use it.
Now you'd just refer to those time periods as "Asian hours" and "European hours." Also, remember there is not 1 stock market. There are somewhere around 50-60 exchanges where a company's stock may be traded (counting dark pools), and each of those may have different rules/open periods/etc.