Migration of trans-Neptunian objects to the Earth is considered. Due to the gravitational influence of large trans-Neptunian objects and mutual collisions, some objects can get such orbits, from which they can be moved inside the Solar System under the gravitational influence of planets. About 10-20% or even more 1-km Earth-crossers could have come from the Edgeworth-Kuiper belt and can move in Jupiter-crossing orbits. The number of former trans-Neptunian objects that cross the Earth's orbit moving in orbits with aphelia inside Jupiter's orbit can be of the same order of magnitude. A total mass of icy planetesimals delivered to the Earth during formation of the giant planets can be about the mass of the Earth's oceans.

Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of increasingly accurate astro-cosmological observations, especially the recent observations of the cosmic microwave background radiation. An overview of the basic context of cosmic topology, the detectability constraints from recent observations, as well as the main methods for its detection and some recent results are briefly presented.