In mathematics, a pointed space is a topological space X with a distinguished basepoint x0 in X. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e. a continuous map f : X → Y such that f(x0) = y0. This is usually denoted
- f : (X, x0) → (Y, y0).
Pointed spaces are important in algebraic topology, particularly in homotopy theory, where many constructions, such as the fundamental group, depend on a choice of basepoint.
The pointed set concept is less important; it is anyway the case of a pointed discrete space.
Read more about Pointed Space: Category of Pointed Spaces, Operations On Pointed Spaces
Famous quotes containing the words pointed and/or space:
“I heard the beat of centaur’s hoofs over the hard turf
As his dry and passionate talk devoured the afternoon.
“He is a charming man” “But after all what did he mean?”—
“His pointed ears. ... He must be unbalanced,”—
“There was something he said that I might have challenged.””
—T.S. (Thomas Stearns)
“When Paul Bunyan’s loggers roofed an Oregon bunkhouse with shakes, fog was so thick that they shingled forty feet into space before discovering they had passed the last rafter.”
—State of Oregon, U.S. public relief program (1935-1943)