We could use is to communicate essentially the same idea:
The condition that a function is continuous is (some declaration).
The reason you question the use of be in the fragment is likely that it is an example of a use of the subjunctive mood, which is an often invisible feature of English.
We use the subjunctive to talk about things that are more like mental ideas than factual realities. Dividing utterences into these two categories is often a tricky enterprise.
That a function is continuous is put forth as more of an idea than a factual reality. The idea is issued as a supposition, and we can use the subjunctive mood to communicate such an idea, though we do not always need to.
The subjunctive is often in operation but not noticeable, because in English the subjunctive often appears identical in form to the indicative mood, which (perhaps we can say) more plainly or ordinarily refers to "real", more tangible things.
I will borrow description and examples from the current Wikipedia article on the English sunjunctive, located at:
He sees a doctor once a year.
This is an example of a use of the verb see in the indicative mood. As you likely expect, see is inflected to sees because it's used with the third-person singular, he.
It is important (that) he see a doctor immediately!
The idea here is different because it describes an opinion or idea that exists in the speaker's mind, not an action or event that we can find in the real world.
Because the subjunctive is in use, we do not change see to sees.
It's important that they see a doctor immediately!
We might say that the subjunctive is likely in use because it is likely an opinion or belief, but the form is the same as if it were a use of see in the indicative. In this rather common situation, the operation of the subjunctive is not visible.
Since verbs in the subjunctive appears in unexpected forms only in certain situations, it can surprise and puzzle learners.
One of the ways that the subjunctive appears as noticeable in form is with use of the verb be.
In the example you encountered, be is not changed to is because the grammar of the subjunctive mood differs from that of the indicative.
Yes. There are other verbs with which we use be in the subjunctive and where be does not change form as in the indicative:
I suggest (that) he be taught some manners.
I demand (that) she be promoted.
If that be the case, we should leave.