A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy defined continuity of $${\displaystyle y=f(x)}$$ as follows: an infinitely small increment 查看更多內容

The concept of continuous real-valued functions can be generalized to functions between metric spaces. A metric space is a set $${\displaystyle X}$$ equipped with a function (called 查看更多內容

If $${\displaystyle f:S\to Y}$$ is a continuous function from some subset $${\displaystyle S}$$ of a topological space $${\displaystyle X}$$ then a continuous … 查看更多內容

• Dugundji, James (1966). Topology. Boston: Allyn and Bacon. ISBN 978-0-697-06889-7. OCLC 395340485.
• "Continuous function" 查看更多內容

Definition
A real function, that is a function from real numbers to real numbers, can be represented by a 查看更多內容

Another, more abstract, notion of continuity is continuity of functions between topological spaces in which there generally is no … 查看更多內容

• Continuity (mathematics)
• Absolute continuity
• Dini continuity
• Equicontinuity 查看更多內容