Question

4. (a) The union of a collection of connected subspaces of X that have a point in common is connected​

Answer 1

Answer:

The union of collection of connected subspaces of X that have a point in common is connected. Proof. Let {Aα} be a collection of connected subspaces of space X. Let p be a point which is common to all Aα i.e., p ∈ Aα.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

• If the intersection of two linked sets in a space is nonempty, the union is connected.
• (Assume that X Y contains a point p and that X and Y are connected.)
• If X Y is the union of two disjoint sets A and B, both of which are open in A and B, then p belongs to either A or B, say A.