Sentence examples for be continuous at a from inspiring English sources

(4 A self mapping is said to be continuous at a point, if implies that for every in.

A function (f: Xrightarrow Z ) is said to be continuous at a point (x_{0} in X).

(2) Now, let F : T → clos ( X ) be continuous at a point t 0 in the metric ρ cl.

A mapping (fcolon Xto Y) is said to be continuous at a point (xin X) if (f(x_{n}) rightarrow f(x)).

A mapping (T:X rightarrow X) is said to be continuous at a point (xin X), if for every (varepsilon>0) there exists a (delta>0) such that (T(B_{sigma_{b}} x,delta))subseteq B_{sigma_{b}}(Tx,varepsilon)).

A function f : X → Y is said to be continuous at a point x 0 ∈ X if, for any sequence { x n } in X converging to x 0, the sequence { f ( x n ) } in Y converges to f ( x 0 ).

A mapping (T Arightarrow B) is said to be continuous at (xin A) if for every sequence ((x_{n})) in A that converges to x, the sequence ((Tx_{n})) in B converges to Tx.

Continuous functions preserve limits; that is, a function f is continuous at a point p if the limit of f(t) as t approaches p is equal to f(p).

If is continuous at a given, then.

Suppose that is continuous at a point.

So f is continuous at a. Since a is arbitrary, hence f is continuous.