Hausdorff Dimension Infinity
What are some examples of non-trivial metric spaces that have Hausdorff Dimension of infinity?
I could only think of $mathbb{R}$ with the discreet metric.
real-analysis hausdorff-measure
asked Nov 26 at 18:53
PhysMath
343111
add a comment |
What are some examples of non-trivial metric spaces that have Hausdorff Dimension of infinity?
I could only think of $mathbb{R}$ with the discreet metric.
real-analysis hausdorff-measure
asked Nov 26 at 18:53
PhysMath
343111
2
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20
add a comment |
What are some examples of non-trivial metric spaces that have Hausdorff Dimension of infinity?
I could only think of $mathbb{R}$ with the discreet metric.
real-analysis hausdorff-measure
asked Nov 26 at 18:53
PhysMath
343111
What are some examples of non-trivial metric spaces that have Hausdorff Dimension of infinity?
I could only think of $mathbb{R}$ with the discreet metric.
real-analysis hausdorff-measure
real-analysis hausdorff-measure
asked Nov 26 at 18:53
PhysMath
343111
asked Nov 26 at 18:53
PhysMath
343111
asked Nov 26 at 18:53
PhysMath
343111
asked Nov 26 at 18:53
PhysMath
343111
asked Nov 26 at 18:53
PhysMath
343111
343111
2
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20
add a comment |
2
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20
2
2
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20
add a comment |
1 Answer
1
active
oldest
votes
Take the separable Hilbert space of infinite dimension
$$
ell^2={(a_n)_{ninmathbb{N}}subseteq mathbb{R}:sum_{ninmathbb{N}}a_n^2<infty}
$$
answered Nov 26 at 19:21
Dante Grevino
90819
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Take the separable Hilbert space of infinite dimension
$$
ell^2={(a_n)_{ninmathbb{N}}subseteq mathbb{R}:sum_{ninmathbb{N}}a_n^2<infty}
$$
answered Nov 26 at 19:21
Dante Grevino
90819
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
add a comment |
Take the separable Hilbert space of infinite dimension
$$
ell^2={(a_n)_{ninmathbb{N}}subseteq mathbb{R}:sum_{ninmathbb{N}}a_n^2<infty}
$$
answered Nov 26 at 19:21
Dante Grevino
90819
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
add a comment |
Take the separable Hilbert space of infinite dimension
$$
ell^2={(a_n)_{ninmathbb{N}}subseteq mathbb{R}:sum_{ninmathbb{N}}a_n^2<infty}
$$
answered Nov 26 at 19:21
Dante Grevino
90819
Take the separable Hilbert space of infinite dimension
$$
ell^2={(a_n)_{ninmathbb{N}}subseteq mathbb{R}:sum_{ninmathbb{N}}a_n^2<infty}
$$
answered Nov 26 at 19:21
Dante Grevino
90819
edited Dec 6 at 3:19
answered Nov 26 at 19:21
Dante Grevino
90819
answered Nov 26 at 19:21
Dante Grevino
90819
answered Nov 26 at 19:21
Dante Grevino
90819
90819
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
add a comment |
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
1
1
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
+1 Did you know that the subset of $ell^2$ with all rational coordinates has Hausdorff dimension 1? One of my favorite results of Erdos.
– Mark McClure
Nov 27 at 0:23
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
No, I never studied the Hausdorff measure in depth. It's an interesting result, thanks for share it!
– Dante Grevino
Nov 27 at 15:57
add a comment |
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2
This frequent Mathematics Stack Exchange user's Ph.D. dissertation is a good place to look. (Hope he doesn't mind my pointing this out!)
– Dave L. Renfro
Nov 26 at 20:12
@DaveL.Renfro No problem!
– Mark McClure
Nov 27 at 0:20