An adverb for all possibilities/possible options?

Question

I want an adverb for the following blank. The adverb is used when we want to say that the options/possibilities we are gonna talk about exhaust all options/possibilities.

A and B are all the factors that are relevant to the problem X. Therefore, ----- there are 3 possible ways to explain the problem X: 1) A causes it; 2) B causes it; and 3) A and B both cause it.

I remember that I saw somewhere the word topologically, or a word similar to that, was used in the sense mentioned above.Topologically has not such a sense according to the dictionaries I saw, and I couldn't find any word similar to it.

Answer 1

An old thread, I know, but worth adding to. You're trying to work with sets here, so you need to define a set of all possibilities. Having defined that set, you can then define its members. By using "consists" (e.g. "The set consists of..."), you can explicitly (and clearly) define all members of the set

You might want to try e.g. "Therefore, the set of all possible ways to explain the cause of problem X consists of: 1) A causes it; 2) B causes it; and 3) both A and B cause it."

Answer 2

Definitely not topologically which means according to Merriam Webster:

1: topographic study of a particular place; specifically :the history of a region as indicated by its topography 2 a (1) :a branch of mathematics concerned with those properties of geometric configurations (such as point sets) which are unaltered by elastic deformations (such as a stretching or a twisting) that are homeomorphisms (2) :the set of all open subsets of a topological space]

Words you might use are: "completely", "comprehensively", or perhaps best of all "exclusively."

Therefore, there are exclusively 3 possible ways to explain the problem X: 1) A causes it; 2) B causes it; and 3) A and B both cause it.

Or another possibility is "exactly", in this specific context:

Therefore, there are exactly 3 possible ways to explain the problem X: 1) A causes it; 2) B causes it; and 3) A and B both cause it.

Answer 3

The word I was looking for is typologically

typology: the systematic classification of the types of something according to their common characteristics
_{definition from wiktionary}