What technology allows for shared network resources for Time Machine users?

The technology that allows for shared network resources for Time Machine users is Time Capsule or compatible devices. Time Machine, Apple's backup software, can use a variety of storage options, but for network backups, it needs a device that is specifically designed to work over a network.

Time Capsule is a wireless router that includes a built-in hard drive, enabling Mac users to back up their data over Wi-Fi seamlessly. This convenience eliminates the need for local connections, allowing multiple Macs to back up to the same resource over the network. Furthermore, compatible devices may include any network-attached storage (NAS) systems that support Time Machine. These devices offer a centralized location for backups, making it easier for users to manage their data and for the system to restore information as needed.

Other options mentioned do not provide the same functionality. Local storage and USB drives require a direct connection to the device, preventing shared access. Internal disk storage is limited to the individual Mac, which likewise does not support shared network use. Therefore, the optimal solution for shared network backups with Time Machine is through Time Capsule or similar compatible devices.