Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options questions only not deleted user 58682

Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.

2 votes
0 answers
79 views

Associated barrelled topology of norm topology on $C_c(X)$

Let $X$ be a locally compact Hausdorff space, $C(X; K)$ the Banach space of continuous functions on $X$ with support in $K$, for compact $K \subseteq X$, and $C_c(X) = \lim_K C(X; K)$ the locally conv …
yada's user avatar
  • 1,773
0 votes
0 answers
94 views

Non-B-completeness of finest locally convex topology

For an index set $A$ consider the locally convex direct sum $X_A := \bigoplus_{\alpha \in A} \mathbb{R}_\alpha$ of $|A|$-many lines $\mathbb{R}_\alpha = \mathbb{R}$. Then $X_A$ is complete. It is know …
yada's user avatar
  • 1,773
7 votes
1 answer
596 views

Is the equicontinuous weak-star topology locally convex on the dual of an LF-space?

The Banach-Dieudonné theorem states that if $X$ is a metrizable locally convex Hausdorff space then the equicontinuous weak-* topology $ew^*$ on $X'$ coincides with the topology of precompact converge …
yada's user avatar
  • 1,773
11 votes
2 answers
1k views

Do Hausdorff locally convex inductive limits always exist?

The following is from Schaefer, "Topological Vector Spaces", 1999, p. 56/57: Let $(E_\alpha)_{\alpha \in A}$ be a family of locally convex spaces with $\alpha$ in a directed poset $A$ and $h_{\beta \ …
yada's user avatar
  • 1,773