A topology table is used by routers that route traffic in a network. It consists of all routing tables inside the Autonomous System

Autonomous system (Internet)

Within the Internet, an Autonomous System is a collection of connected Internet Protocol routing prefixes under the control of one or more network operators that presents a common, clearly defined routing policy to the Internet....

 where the router is positioned. Each router using the routing protocol EIGRP then maintains a topology table for each configured network protocol — all routes learned, that are leading to a destination are found in the topology table. EIGRP must have a reliable connection.