advanced mathematics

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Across
  1. 3. A point in the domain of a function where all partial derivatives are zero, but which is not a local extremum.
  2. 5. A mapping between topological spaces that is continuous, bijective, and has a continuous inverse; essentially a "topological isomorphism."
  3. 8. The most famous "unsolved" conjecture regarding the distribution of zeros of the zeta function.
Down
  1. 1. The "kernel" of a linear transformation; the set of all vectors that map to the zero vector.
  2. 2. A collection of sets where the intersection of any two sets in the collection is empty.
  3. 4. A group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
  4. 6. A prime p such that 2^p - 1 is also prime.
  5. 7. A sequence where the terms become arbitrarily close to each other as the sequence progresses.
  6. 8. The algebraic structure consisting of a set equipped with two binary operations satisfying specific axioms (e.g., integers under addition and multiplication).