from typing import List


def find_closest_pair_1d(points: List[float]) -> List[float]:
    """
    Finds the closest pair in the given 1D points.
    :param points: list[float]
    :return: list[float]
    """
    # Check whether the input point list is null or empty
    if not points:
        return []

    if len(points) == 1:
        return []

    # Sort the points   [O(nlog n)]
    points.sort()
    # The closest pair must be adjacent in the ordering.

    # Iterate over the adjacent pairs, and find the closest pair   [O(n)]
    p1, p2 = points[0], points[1]
    min_distance = points[1] - points[0]
    for i in range(1, len(points) - 1):
        if points[i + 1] - points[i] < min_distance:
            p1, p2 = points[i], points[i + 1]
            min_distance = points[i + 1] - points[i]
    return [p1, p2]