Was the roman empire in any way related to the Ottoman Empire?

Question

if so, does that mean, they survived all the way to the twentieth century?

Answer 1

No. The Turks conquered the Eastern Roman or Byzantine Empire in the mid 15th century. They then developed into the Ottoman Empire later on. You could then argue that the Ottomans were responsible for the final destruction or fall of the Roman Empire.
Historian

Answer 2

No, unless you mean the Eastern Empire, called Byzantine, which the Ottomans put to final death in the mid 15th century.

The true Roman Empire had expired through invasions by various Germanic tribes several centuries before the Ottoman Turks made their way out of central Asia.

Answer 3

Sort of.
The Roman Empire was divided into East (Byzantium) and West (Rome, Italy). Old Rome fell in 476, while New Rome (Constantinople) thrived for another 700 years, and continued until 1453, when it was conquered by the Ottoman Empire. Also, when Kievan Rus (medieval Russia) converted to Christianity, it did so through Constantinople. Thus, the Tsars of Russia saw themselves as inheritors of the legacy of Byzantium. Nicholas II (d. 1918) was, in a real historical manner of speaking, the last of the Byzantine Emperors.