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.

7 мар. 2019 г. · When he gets to defining the inductive limit topology on a certain space, it seems unnecessarily abstruse and confusing to me.

4 апр. 2018 г. · Both of these topologies have universal properties characterizing continuous maps out of V: In the first case, this universal property holds ...

31 мар. 2021 г. · The author goes on to define the inductive limit topology as follows: First, we define B to be the collection of all the balanced convex sets V.

27 июл. 2014 г. · The topology of Φ is by definition inductive topollogy, i.e. the strongest locally convex topology, in which the embeddings Φi→Φ are continuous.

24 апр. 2024 г. · A neighborhood of a point always contains an open neighborhood of the same point, so the proof with open neighborhoods does not restrict ...

29 мая 2023 г. · We are given a topological space X together with family of sub-spaces Xi which cover the whole space. We are also given a subset D⊂X, such that, ...

27 июн. 2017 г. · It's a recursive definition. We define all the spaces of dimension −1: we define there to be only one, the empty set with its one and only topology.

18 июл. 2014 г. · The inductive limit topology is the one induced by the family {μW:W∈U} (the construction of a locally convex topology from a family of seminorms ...

9 апр. 2014 г. · There also is the inductive limit topology on E′, that is the finest locally convex topology such that every E′n⊂E′ is continuous.