Puzzle for You

123456789101112
Across
  1. 3. A structure-preserving map between two algebraic structures, such as groups or rings
  2. 6. A line that a curve approaches as it heads towards infinity but never actually touches
  3. 7. The process of determining the area under a curve, often linked with integration
  4. 9. A function that is both injective and surjective, establishing a one-to-one correspondence between two sets
  5. 10. A topological space that locally resembles Euclidean space, often used in complex geometry
  6. 12. A mapping between two structures that preserves operations and relations, implying structural similarity
Down
  1. 1. A curve obtained as the intersection of a cone with a plane
  2. 2. A scalar associated with a linear transformation that, when multiplied by an eigenvector, results in the same vector scaled
  3. 4. Describes vectors that are perpendicular to each other, with a dot product of zero
  4. 5. A type of conic section with two distinct branches, formed when a plane intersects both halves of a double cone
  5. 8. An equation that requires integer solutions, often involving multiple variables
  6. 11. A mathematical object generalizing scalars, vectors, and matrices, used in multilinear algebra