What is the meaning of Homotopy?

A continuous deformation of one continuous function or map to another.

The relationship between two continuous functions where homotopy from one to the other is evident.

Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes).

A theory associating a system of groups with each topological space.

A system of groups associated with a topological space.

Source: wiktionary.org