A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the separation axioms, nor for metrizability. Being a discrete space, however, is a divisible property.
See alsoHereditary Property, Productive Property
This entry contributed by Margherita Barile
Explore with Wolfram|Alpha
ReferencesJoshi, K. D. Introduction to General Topology. New Delhi, India: Wiley, p. 128, 1983.Kelley, J. L. General Topology. New York: Van Nostrand, p. 133, 1955.
Referenced on Wolfram|AlphaDivisible Property
Cite this as:
Barile, Margherita. "Divisible Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DivisibleProperty.html