Comb Space


The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) and (1/n,1) for all positive integers n.

With respect to the relative topology C is pathwise-connected. It is therefore connected, but not locally pathwise-connected at any point of the open interval (0,1) since each open disk centered at point one of these points intersects S in a union of parallel segments, forming a disconnected set.

See also

Broom Space

This entry contributed by Margherita Barile

Explore with Wolfram|Alpha


Joshi, K. D. Introduction to General Topology. New Delhi, India: Wiley, p. 151, 1983.

Referenced on Wolfram|Alpha

Comb Space

Cite this as:

Barile, Margherita. "Comb Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications