Deformation retract

A deformation retract is a way of transforming one shape into another shape smoothly, where the final shape is a part of the original shape. Imagine a bouncy rubber band—you can stretch and squish it without tearing or cutting. If you can continuously pull and push the rubber band so it eventually fits perfectly around a smaller section of itself and that smaller section is significant in some sense, you've created a deformation retract. This concept is important in mathematics, particularly in topology, where it helps in understanding the essential features of spaces by simplifying them while retaining key properties.