Continuous Function
A continuous function is a Function 
where the pre-image of every Open Set in 
is Open in 
. A function 
in a single variable 
is said to be continuous at point 
if
- 1.
is defined, so that is in the Domain of 
. - 2.
exists for in the Domain of . - 3.
,
is Differentiable at point , then it is also continuous at . If and 
are continuous at , then- 1.
is continuous at . - 2.
is continuous at . - 3.
is continuous at . - 4.
is continuous at if 
and is discontinuous at if 
. - 5.
is continuous at , where denotes 
, the Composition of thefunctions and .
- Itô's Lemma
- Itô's Theorem
- Iverson Bracket
- Iwasawa's Theorem
- j
- Jackson's Difference Fan
- Jackson's Identity
- Jackson's Theorem
- Jacobi Algorithm
- Jacobian
- Jacobian Conjecture
- Jacobian Curve
- Jacobian Determinant
- Jacobi-Anger Expansion
- Jacobian Group
- Jacobi Differential Equation
- Jacobi Differential Equation (Calculus of Variations)
- Jacobi Elliptic Functions
- Jacobi Function of the First Kind
- Jacobi Function of the Second Kind
- Jacobi-Gauss Quadrature
- Jacobi Identities
- Jacobi Matrix
- Jacobi Method
- Jacobi Polynomial