Can the /// access the Internet?

You bet! The /// and its communications software is definitely
equal to the task of accessing an Internet host to "surf the
Internet". In fact, internet access via the /// is both viable and
enjoyable. The lack of graphics seldom is a barrier.

The world's most popular Internet hosts are still Unix computer
systems. Unix systems have traditionally integrated well into the
Internet, and plenty of text-based Internet software is available on
these hosts to enable your Apple /// to become a powerful Internet