**Explanation:**

The given statement states that AB is equal to BC. Let's understand this statement and its implications in detail.

**Understanding the Statement:**
- AB = BC means the length of line segment AB is equal to the length of line segment BC.
- In simpler terms, the distance between point A and point B is the same as the distance between point B and point C.

**Implications:**
- If AB = BC, it implies that the triangle ABC is an isosceles triangle.
- An isosceles triangle is a triangle that has two sides of equal length.
- In this case, since AB = BC, the triangle ABC has two sides AB and BC that are equal.
- The third side AC can be of any length.

**Explanation of Options:**
a) A ≠ C: This option states that point A is not equal to point C. However, the given statement AB = BC does not provide any information about the equality of points A and C. So, this option is incorrect.
b) C ≠ A: This option states that point C is not equal to point A. Similar to the explanation for option a), the given statement AB = BC does not provide any information about the equality of points A and C. So, this option is incorrect.
c) A = C: This option states that point A is equal to point C. The given statement AB = BC does not directly mention anything about the equality of points A and C. However, since AB = BC, it implies that the two sides of the triangle ABC (AB and BC) are equal. And in an isosceles triangle, the angles opposite to the equal sides are also equal. So, angle A = angle C. Therefore, this option is correct.
d) B ≠ C: This option states that point B is not equal to point C. Similar to the explanation for option a), the given statement AB = BC does not provide any information about the equality of points B and C. So, this option is incorrect.

Therefore, the correct answer is option 'C' - A = C.