True or False:Let $X$ be a topological space such that any two nonempty openset in $X$ intersect, then $X$ is...
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Let $X$ be a topological space such that any two nonempty open sets in $X$ intersect,then $X$ is compact. True /false
?
I don't know how to think about this problem.
Any hints/solution ?
general-topology
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
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closed as off-topic by Alexander Gruber♦ Dec 4 '18 at 4:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $X$ be a topological space such that any two nonempty open sets in $X$ intersect,then $X$ is compact. True /false
?
I don't know how to think about this problem.
Any hints/solution ?
general-topology
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
$endgroup$
closed as off-topic by Alexander Gruber♦ Dec 4 '18 at 4:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
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False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
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– Poon Levi
Dec 3 '18 at 5:27
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@PoonLevi Why not an official answer?
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– Paul Frost
Dec 3 '18 at 9:13
add a comment |
$begingroup$
Let $X$ be a topological space such that any two nonempty open sets in $X$ intersect,then $X$ is compact. True /false
?
I don't know how to think about this problem.
Any hints/solution ?
general-topology
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
$endgroup$
Let $X$ be a topological space such that any two nonempty open sets in $X$ intersect,then $X$ is compact. True /false
?
I don't know how to think about this problem.
Any hints/solution ?
general-topology
general-topology
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
edited Dec 3 '18 at 5:09
Thomas Shelby
2,189220
2,189220
asked Dec 3 '18 at 0:34
santoshsantosh
1019
asked Dec 3 '18 at 0:34
santoshsantosh
1019
asked Dec 3 '18 at 0:34
santoshsantosh
1019
1019
closed as off-topic by Alexander Gruber♦ Dec 4 '18 at 4:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Alexander Gruber♦ Dec 4 '18 at 4:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
$endgroup$
– Poon Levi
Dec 3 '18 at 5:27
$begingroup$
@PoonLevi Why not an official answer?
$endgroup$
– Paul Frost
Dec 3 '18 at 9:13
add a comment |
$begingroup$
False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
$endgroup$
– Poon Levi
Dec 3 '18 at 5:27
$begingroup$
@PoonLevi Why not an official answer?
$endgroup$
– Paul Frost
Dec 3 '18 at 9:13
$begingroup$
False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
$endgroup$
– Poon Levi
Dec 3 '18 at 5:27
$begingroup$
False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
$endgroup$
– Poon Levi
Dec 3 '18 at 5:27
$begingroup$
@PoonLevi Why not an official answer?
$endgroup$
– Paul Frost
Dec 3 '18 at 9:13
$begingroup$
@PoonLevi Why not an official answer?
$endgroup$
– Paul Frost
Dec 3 '18 at 9:13
add a comment |
1 Answer
1
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oldest
votes
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The statement is false. Consider the topology over $mathbb{N}$ generated by ${{1, k}: kinmathbb{N}}$.
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The statement is false. Consider the topology over $mathbb{N}$ generated by ${{1, k}: kinmathbb{N}}$.
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
$endgroup$
add a comment |
$begingroup$
The statement is false. Consider the topology over $mathbb{N}$ generated by ${{1, k}: kinmathbb{N}}$.
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
$endgroup$
add a comment |
$begingroup$
The statement is false. Consider the topology over $mathbb{N}$ generated by ${{1, k}: kinmathbb{N}}$.
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
$endgroup$
The statement is false. Consider the topology over $mathbb{N}$ generated by ${{1, k}: kinmathbb{N}}$.
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
answered Dec 3 '18 at 23:48
Poon LeviPoon Levi
42137
42137
add a comment |
add a comment |
$begingroup$
False, consider the topology over $mathbb{N}$ generated by ${{1,k}:kinmathbb{N}}$.
$endgroup$
– Poon Levi
Dec 3 '18 at 5:27
$begingroup$
@PoonLevi Why not an official answer?
$endgroup$
– Paul Frost
Dec 3 '18 at 9:13