As already mentioned above a few times now you can't suddenly have some elements that are not affected by the styles you have applied or from inheriting where applicable.
After all that is exactly what "cascading" style sheets are all about and there isn't a mechanism to turn this off (although some times it would be useful).
If you haven't defined any global or descendant selectors and have styled all your page using classes or ids direct on the elements concerned then all you would need to worry about would be the properties that were inherited from the parent. Although that negates a lot of the usefulness of css if you take that approach.
Not all properties are inherited and only things like color and font properties (and a few other properties) would be inherited into the child elements (things like borders, backgrounds, padding etc are not inherited).
In answer to your question your best option is to style the elements in that section as you want them to appear.