What does it mean to say that a topology is defined by a metric?
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
add a comment |
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43
add a comment |
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
I have read the following phrase. The weak topology on $X$ is defined by a translation invariant metric. What does this mean? Does this mean that the weak topology is the same as the topology that the metric induces?
general-topology
general-topology
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
edited Nov 22 '18 at 4:04
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
asked Nov 22 '18 at 4:02
伽罗瓦
1,083615
1,083615
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43
add a comment |
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43
add a comment |
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It means that the weak topology isn't the same as the topology that a metric of this type induces.
– Lord Shark the Unknown
Nov 22 '18 at 4:03
Oops. Ok thanks! Edited for clarity.
– 伽罗瓦
Nov 22 '18 at 4:03
Your interpretation is plausible, but without more context, it's hard to say whether it's correct. Where does the metric come from?
– Hew Wolff
Nov 22 '18 at 4:43