Preimage example sentences

"Preimage" Example Sentences

1. The preimage of a function can be found by inverting the equation.
2. The set of points that map to a particular point is called the preimage.
3. The preimage of a closed set under a continuous function is closed.
4. The preimage of an open set under a continuous function is open.
5. The preimage of a subset of the range of a function may not be a subset of the domain.
6. A bijective function has a unique preimage for each point in the range.
7. The preimage of the empty set under any function is the empty set.
8. In topology, the preimage of a neighborhood is called an open set.
9. The preimage of a function can be thought of as the "backwards" mapping.
10. A function is injective if and only if each element in the range has a unique preimage.
11. A function is surjective if and only if each element in the range has at least one preimage.
12. The preimage of a function is also known as the inverse image.
13. In linear algebra, the null space of a matrix can be thought of as the preimage of the zero vector.
14. The preimage of a function may not be a function itself.
15. The preimage of a function is denoted by f^-1(B), where B is a subset of the range of the function.
16. A continuous function maps connected sets to connected sets, and their preimages are also connected.
17. The preimage of a regular value of a smooth function is a submanifold of the domain.
18. A function is bijective if and only if it has a well-defined preimage for each point in the range.
19. The preimage of a function is larger than its image.
20. In algebraic geometry, the Zariski preimage is used to define fibered products.
21. The preimage of a singleton set under a function is called a fiber.
22. The preimage of the range of a function is the entire domain.
23. The preimage of a finite set under a continuous function is finite.
24. The preimage of a connected set under a continuous function is connected.
25. A function is invertible if and only if its preimage is a function.
26. The preimage of a function is a set, not a function itself.
27. The preimage of a closed set may not be closed.
28. The preimage of an open set may not be open.
29. The preimage of a function is unique.
30. A continuous function maps compact sets to compact sets, and their preimages are also compact.

Common Phrases

1. Finding the preimage of a function;
2. Inverse image or preimage of a set;
3. Computing the preimage of a point;
4. Determining the preimage of a set under transformation;
5. Inverse mapping or preimage mapping;
6. Preimage of a binary operation;
7. Preimage of a subset;
8. Preimage of a group element;
9. Identifying the preimage of a linear function;
10. Preimage with respect to a continuous function.