4. In space, there are 5 points, the distance between any two points is different, and any 4 points can form three closed broken lines. For each closed broken line formed, the shortest segment is painted red. $A$ is one of the 5 points.
Let the number of red segments starting from point $A$ be $m$;
When no segments starting from point $A$ are colored, the number of uncolored segments is $n$.
Then, the maximum value of $m \times n$ is
Solve step by step for the maximum value of \( m \):
Consider 5 points \( A, B, C, D, E \). The line segments \( AB, AC, AD, AE \) can all be colored red. Without loss of generality, assume \( AB < AC < AD < AE \). If \( AE \) is also colored red, then it must be the shortest side of some closed broken line, but any closed broken line containing \( AE \) must also contain another line segment from point \( A \), making \( AE \) shorter than this segment, which contradicts the fact that \( AE \) is the longest segment from point \( A \).

On the other hand, among the 4 line segments from point \( A \), 3 can be red. An example is omitted. Therefore, the maximum value of \( m \) is 3.
Next, find the maximum value of \( n \).
Assume the 4 line segments from point \( A \) are all colored, and we examine the coloring of the 6 line segments between the remaining four points \( B, C, D, E \).

Among these 6 line segments, the maximum number of uncolored segments is 2. Otherwise, if there are 3 uncolored segments, then at least two of these segments must share a common endpoint. Without loss of generality, assume \( BC \) and \( BD \) are uncolored. Then, the closed broken line \( A-C-B-D-A \) would have no colored edges, which is a contradiction.

On the other hand, a configuration can be constructed where \( BD \) and \( CE \) do not need to be colored. For example, let \( BD = 7 \), \( CE = 9 \), and \( BD \perp CE \). Assume \( BE = 5 \), \( DE = 4\sqrt{2} \), \( BC = \sqrt{34} \), and \( CD = \sqrt{41} \). When point \( A \) is sufficiently far from \( B, C, D, E \), coloring \( BE, DE, BC, \) and \( CD \) red satisfies the problem's conditions.

Therefore, the maximum value of \( n \) is 6.