In this paper we describe a compact set in which is typical from the point of view of Baire categories, as it appears when seen from some point of . It matters whether belongs to or not! If , then looks porous (this is easily seen). If , then looks only -porous, but dense at least in a half-sphere (of directions from ). If is a typical point of , then looks even dense (in the whole sphere).
Tudor ZAMFIRESCU. "The strange aspect of most compacta." J. Math. Soc. Japan 57 (3) 701 - 708, July, 2005. https://doi.org/10.2969/jmsj/1158241930