Mixing
relative interiors of a k dimensional simplex
Clash Royale CLAN TAG#URR8PPP
up vote
-1
down vote
favorite
Can anyone prove that the relative interior of a k dimensional simplex is nonempty?
I've found a proof for that which was based on the properties of a continuous function but I couldn't understand the details.
analysis convex-analysis
asked Jul 23 at 9:10
Farzam
11
add a comment |Â
up vote
-1
down vote
favorite
Can anyone prove that the relative interior of a k dimensional simplex is nonempty?
I've found a proof for that which was based on the properties of a continuous function but I couldn't understand the details.
analysis convex-analysis
asked Jul 23 at 9:10
Farzam
11
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Can anyone prove that the relative interior of a k dimensional simplex is nonempty?
I've found a proof for that which was based on the properties of a continuous function but I couldn't understand the details.
analysis convex-analysis
asked Jul 23 at 9:10
Farzam
11
Can anyone prove that the relative interior of a k dimensional simplex is nonempty?
I've found a proof for that which was based on the properties of a continuous function but I couldn't understand the details.
analysis convex-analysis
asked Jul 23 at 9:10
Farzam
11
edited Jul 23 at 11:07
asked Jul 23 at 9:10
Farzam
11
asked Jul 23 at 9:10
Farzam
11
asked Jul 23 at 9:10
Farzam
11
11
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16
add a comment |Â
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2860158%2frelative-interiors-of-a-k-dimensional-simplex%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
I think it is easy to prove by induction if you know the recursive definition of a simplex. Sketch - a k-1 has an internal point, move it to the k'th dimension to get an internal point of a k-dimensional simplex.
– Shachar Har-Shuv
Jul 23 at 9:16