Are there spaces where barreled sets are $0$-neighborhoods but which are not locally convex?
If $X$ is a linear topological space, without being locally convex, is it possible that every barreled set in $X$ (closed+convex+circled+absorbing) is a neighborhood of the origin?
general-topology
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
add a comment |
If $X$ is a linear topological space, without being locally convex, is it possible that every barreled set in $X$ (closed+convex+circled+absorbing) is a neighborhood of the origin?
general-topology
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
add a comment |
If $X$ is a linear topological space, without being locally convex, is it possible that every barreled set in $X$ (closed+convex+circled+absorbing) is a neighborhood of the origin?
general-topology
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
If $X$ is a linear topological space, without being locally convex, is it possible that every barreled set in $X$ (closed+convex+circled+absorbing) is a neighborhood of the origin?
general-topology
general-topology
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
edited Nov 26 '18 at 8:53
Tianlalu
3,09621038
3,09621038
asked Nov 26 '18 at 7:19
Maxim Diana
112
asked Nov 26 '18 at 7:19
Maxim Diana
112
asked Nov 26 '18 at 7:19
Maxim Diana
112
112
add a comment |
add a comment |
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