The set of possible names allowed in a given environment. The POSIX name space, which follows hierarchical file system syntax (i.e., \sys\pub\myfile) is distinct from the MPE/iX name space, which follows MPE naming rules (i.e., MYFILE.PUB.SYS).
Each time you want to add a different type of machine in a network, such as a Macintosh, an OS/2-based machine, or a UNIX based machine, you have to provide for file compatibility with the network operating system. You do this with name spaces loaded on the file server (as NLMs with NetWare) that regulate the cross-network conversation that take place.
The scope within which a name provides the intended identification. Here is an analogy: given names are intended to uniquely identify members of a family; in this case, the name space is the family.