Answer to Question #217094 in Differential Geometry | Topology for Prathibha Rose

Question

Determine the components of T1 zero dimensional space

Answer 1

Solution:

A space is zero-dimensional if it is T₁ and has a basis consisting of clopen sets, and totally disconnected if the quasicomponents of all points (intersections of all clopen neighborhoods) are singletons.

Thus, its component is a basis consisting of clopen sets.