Question
Solution Preview
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.
When we think of a connected set A in the plane we think that it means that between any two points x and y in A we can find a continuous path with x as beginning and y as end point, that is totally contained in A. Topologists call this property "path connected", and have another definition of connected: A is connected if we can not write A as the disjoint union of sets B and C that are disjoint and open in A....