Need assistance,can you imagine a continuously deformation between X and Y?

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In summary, continuous deformation is a gradual change of shape or configuration of an object without any abrupt breaks or discontinuities. It maintains the connectivity and topology of the original object. Not all objects can have a continuous deformation between them, as they must have similar topology and connectivity. Continuous deformation is related to transforming one object into another through a gradual change in shape or configuration. Factors such as topology, connectivity, material properties, and external forces can affect the possibility of a continuous deformation between objects. Some real-life examples of continuous deformations include stretching a rubber band, bending a wire, and folding a piece of paper.
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kakarotyjn
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how can X be continuously deformed to Y?
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Yes:
Let X be a ball , i.e., the interior of a circle (either a s astand-alone space, or

embedded in R^n), and let Y be, say, the center of the ball . Can you see how

to deform X into Y continuously.?. Can you see why, e.g., a circle could not be

deformed to a point (i.e., to a 1-pt. subspace of the circle.)?
 

FAQ: Need assistance,can you imagine a continuously deformation between X and Y?

What is a continuous deformation?

A continuous deformation refers to the gradual change of shape or configuration of an object without any abrupt breaks or discontinuities. It is a smooth transformation that maintains the connectivity and topology of the original object.

Can any two objects have a continuous deformation between them?

No, not all objects can have a continuous deformation between them. The objects must have similar topology and connectivity in order for a continuous deformation to exist.

How is continuous deformation related to X and Y?

Continuous deformation is the concept of transforming one object into another through a gradual change in shape or configuration. X and Y represent two different objects that are connected through a continuous deformation.

What factors can affect the possibility of a continuous deformation between X and Y?

The topology and connectivity of X and Y are the main factors that determine the possibility of a continuous deformation between them. Other factors such as the material properties and external forces can also play a role.

What are some real-life examples of continuous deformations?

Some examples of continuous deformations in everyday life include stretching a rubber band, bending a wire, and folding a piece of paper. These all involve transforming the original shape into a new one without any abrupt breaks or discontinuities.

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