23 февр. 2013 г. · Suppose {fn} is a sequence of mappings from a connected complete metric space X to a metric space Y. Given f:X→Y such that fn(xn)→f(x) whenever ... Uniform convergence of a sequence of continuous functions on ... counterexample sequence of continuous function converges to ... composition of uniformly convergence sequence with ... Does pointwise convergence against a continuous function ... Другие результаты с сайта math.stackexchange.com

22 мар. 2013 г. · We say that fn f n converges continuously to f f at x x if fn(xn)⟶f(x) f n ⁢ ( x n ) ⟶ f ⁢ ( x ) for every sequence (xn)n⊂X ( x n ) n ⊂ X such ...

Universal representations of convergence algebras and some general remarks of function spaces Pages 64-105 PDF

In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence.

Let X be a convergence space and C(X) the i^-algebra of all continuous real-valued functions on X, equipped with the continuous convergence structure.

The theory of continuous convergence (initiated by Hahn and relaunched by Arens and Dugundji) offers a conceptual framework to the present paper. 1.

If fi → f uniformly, then f is continuous, however we know that the limit f is not continuous and thus the convergence cannot be uniform. We can in fact ...

The Continuous Mapping theorem states that stochastic convergence is preserved by continuous functions.

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.

Classical continuous convegence has an unexpectedly elegant formulation in RL. Definition. A filter ¿ on RL is said to c-converge to 0, designated. ¿.