In OSPF v2，We can split the AS into areas. But in standard file rfc2328(http://www.potaroo.net/ietf/rfc/rfc2328.txt), it doesn't indicate whether every router must belong to area. I thought not, but in page29 of rfc2328, I can see this figure:
A sample OSPF area configuration
And the document says thiat RT5 and RT7 are AS boundaty routers, RT5 is internal router and RT7 is area border routers. But the problem is that I can not see any area the two routers belong to.
On
From the diagram it is not very clear to which area RT5 and RT6 belong to. But in the RFC they have mentioned they both i.e. RT5 and RT6 are internal routers.
At the same time, it is not necessary that all the routers must belong to an area. There could be routers in which OSPF is not enabled at all.
Again, the diagram in RFC does not clarify the type of OSPF router for RT5 and RT6.
From the diagram we can see that there is OSPF topology with backbone Area (Area 0) and Areas 1, 2 and 3.
(backbone). Theses are backbone routers and have only the Area 0
(backbone configured)
RT3 and RT4 are routers with interfaces within Area 1 as well as
Area 0 (backbone). So these are ABRs Area Border routers which
connects a certain area to the backbone area. These kind of
routers have configure more than one area (so no there is not
RT7 and RT10 are routers with interfaces within Area 2 as well as Area 0 (backbone). So these are again ABRs Area Border routers.
Speaking of which your statement is correct the BR (vorder router) RT5 is IR - internal router (because it participates only in area 0) and the ABR RT7 is ABR - area boundary router because it has interfaces in area 0 and area 2.