Can a client receive an IP address without having a gateway after a successful DHCP request?

A client can indeed receive an IP address without having a gateway after a successful DHCP request. In a DHCP environment, the primary role of the DHCP server is to assign IP addresses to clients within a specified range. During this process, the client sends a DHCP request, and the server responds with an IP address and other optional information, such as a default gateway, subnet mask, DNS servers, etc.

However, the provision of a gateway is optional. A device can operate within a local network and communicate with other devices using the assigned IP address without needing to route traffic externally, which would require a gateway. Therefore, it is entirely feasible for a DHCP server to provide an IP address without including a gateway option, resulting in the client being able to function on the local network but unable to send traffic outside of it.

In practical scenarios, this might occur in isolated networks where external routing is unnecessary, or in situations where network communication does not require internet access. Thus, the presence of a gateway is not mandatory for the assignment of an IP address via DHCP.