We study the Tychonoff Compactness Theorem for several different definitions of a compact space.

We report a scanning tunnelling microscopy investigation of the emission of dislocations around nanoindentations in the form of dislocation arrangements previously called hillocks , consisting of two pairs of Shockley partial dislocations, each encompassing a stacking fault. The spatial arrangement and size distribution of hillocks around the nanoindentation traces are studied. We show that standard dislocation theory for an isotropic continuum can be used to describe the stability of the hillocks, their size and spatial distribution and the broadening of the (...) corresponding extended dislocations near the surface. A model is proposed in which hillocks originate from the split into dislocations partials of primary perfect dislocation loops punched into the crystal by the scanning tunnelling microscope tip. This model implies the operation of a novel dislocation mechanism involving long-range transport of matter across the surface. (shrink)