I’ve added 4 more methods, what do you think of them?

///
/// Splits TimePeriod
///
/// Any Time (within or out of TimePeriod)
/// 1 or 2 new Elements
public IEnumerable Split(DateTime splitTime)
{
if (splitTime > Start && (!End.HasValue || End.Value > splitTime))
return new TimePeriod[] { new TimePeriod(Start, splitTime), new TimePeriod(splitTime, End) };
else
return new TimePeriod[] { (TimePeriod)this.MemberwiseClone() };
}

///
/// Removes/Substracts onther Timeperiod
///
/// To be substracted
/// returns 0, 1 or 2 new Elements
public IEnumerable Remove(TimePeriod other)
{
List result = new List();

// everything left over
if (!Overlaps(other))
result.Add(new TimePeriod(this.Start, this.End));
// left side or right side or both sides or nothing left over
else
{
// left ok
if (this.Start other.End))
result.Add(new TimePeriod(other.End.Value, this.End));
}
return result;
}

///
/// Compares 2 timelines and returns overlaps
///
/// Timeline1
/// Timeline2
/// new timeline of overlaps
public static IEnumerable GetOverlaps(IEnumerable timePeriods1, IEnumerable timePeriods2)
{
List result = new List();

foreach (TimePeriod t1 in timePeriods1)
{
foreach (TimePeriod t2 in timePeriods2)
{
// t1 eats t2
if (t1.Start = t2.End))
result.Add(new TimePeriod(t2.Start, t2.End));
// t2 eats t1
else if (t1.Start >= t2.Start && (t2.IsInfinite || t1.End <= t2.End))
result.Add(new TimePeriod(t1.Start, t1.End));
// t1 touches t2 on t1's right side
else if (t1.Start t2.Start)
result.Add(new TimePeriod(t2.Start, t1.End));
// t1 touches t2 on t1′s left side
else if (t1.Start > t2.Start && t1.Start < t2.End)
result.Add(new TimePeriod(t1.Start, t2.End));
}
}
return result;
}

///
/// Removes TimePeriods from a timeline
///
/// Timeline
/// TimePeriods that (might) overlap and shall be removed from timeline
/// new timeline without overlaps
public static IEnumerable RemoveOverlaps(IEnumerable timePeriods, IEnumerable overlaps)
{
List result = timePeriods.ToList();

for (int i = 0; i < result.Count; i++)
{
foreach (TimePeriod overlap in overlaps)
{
if (result[i].Overlaps(overlap))
{
// Add rest of clash (if exists) to end to be processed as well
result.AddRange(result[i].Remove(overlap));

// Remove overlapping TimePeriod
result.RemoveAt(i);
}
}
}
return result;
}

Then again, I can’t see much use for (\infty, n] intervals in a business context.