Continuous describes a map 
between topological
spaces for which the preimage of every open
set in 
is an open set in 
. Equivalently, for every point 
and every neighborhood 
of 
, there is a neighborhood 
of 
such that 
. The topological
spaces together with continuous maps as morphisms form a category
(Stacks Project Authors 2026).
Continuous
See also
Absolutely Continuous, Absolutely Continuous Function, Continuity, Continuous Distribution, Continuous Function, Continuous Map, Continuous Space, Differentiable, Jump, Piecewise ContinuousPortions of this entry contributed by Todd Rowland
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References
Jeffreys, H. and Jeffreys, B. S. "Limits of Functions: Continuity." §1.06 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 17-23, 1988.The Stacks Project Authors. "Simplicial Topological Spaces." §85.2 in The Stacks Project, Tag 09VK, 2026. https://stacks.math.columbia.edu/tag/09VK.Referenced on Wolfram|Alpha
ContinuousCite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Continuous." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Continuous.html