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.
Divisible Property
See also
Hereditary Property, Productive PropertyThis entry contributed by Margherita Barile
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References
Joshi, 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|Alpha
Divisible PropertyCite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Divisible Property." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DivisibleProperty.html