The final topology is also the topology that every direct limit in the category of topological spaces is endowed with.

The space E equipped with the inductive topology тind w.r.t. the family {(Eα,тα,iα) : α ∈ A} is said to be the inductive limit of the family of linear subspaces ...

In mathematics, an LF-space, also written (LF)-space, is a topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive ...

The inductive topology тind on E w.r.t. the family 1(Eα,тα,gα) : α 2 Al is the topology generated by the following basis of neighbourhoods of the origin in ...

9 апр. 2013 г. · One can sharpen Alex Ravsky's answer: Recall that a topological vector space is metrizable if and only if it is first countable. What is inductive dimension? - Mathematics Stack Exchange Locally convex inductive limit topology versus cofinal topology Rudin's Construction of Inductive Limit Topology Inductive limit and denseness - Mathematics Stack Exchange Другие результаты с сайта math.stackexchange.com

The existence of inductive linear topologies and the explicit description of one of its O-bases in terms ofO-bases ofthe given spaces form the main topics ...

The existence of inductive linear topologies and the explicit description of one of its 0-bases in terms of 0-bases of the given spaces form the main topics ...

6 окт. 2023 г. · (b) the inductive topology on X is a unique locally convex topology on X having the following property: if Y is a locally convex space, then ...

Statement of the problem. Main results. In the investigation of inductive limits of normed linear spaces it is required in a number of cases to characterize ...