Mixing
Definition: Maximal Metric Segments
$begingroup$
Recall the definition of a metric segment in a metric space $(X,d)$.
Using the definition 'setup' from the article, two questions come to mind:
Is it possible to extend $gamma$ on the left
$$tag 1 gamma_{a^♪}: [a^♪,b] to X text{ with } a^♪ lt a text{?}$$
Is it possible to extend $gamma$ on the right
$$tag 2 gamma_{b^♪}: [a,b^♪] to X text{ with } b^♪ gt b text{?}$$
Definition: A metric segment is said to be maximal if it can't be extended.
I googled and searched but didn't find this idea anywhere.
Has this been pursued in any way?
or
Are there related definitions/theories involving metric spaces?
reference-request metric-spaces soft-question definition
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
$endgroup$
add a comment |
$begingroup$
Recall the definition of a metric segment in a metric space $(X,d)$.
Using the definition 'setup' from the article, two questions come to mind:
Is it possible to extend $gamma$ on the left
$$tag 1 gamma_{a^♪}: [a^♪,b] to X text{ with } a^♪ lt a text{?}$$
Is it possible to extend $gamma$ on the right
$$tag 2 gamma_{b^♪}: [a,b^♪] to X text{ with } b^♪ gt b text{?}$$
Definition: A metric segment is said to be maximal if it can't be extended.
I googled and searched but didn't find this idea anywhere.
Has this been pursued in any way?
or
Are there related definitions/theories involving metric spaces?
reference-request metric-spaces soft-question definition
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
$endgroup$
add a comment |
$begingroup$
Recall the definition of a metric segment in a metric space $(X,d)$.
Using the definition 'setup' from the article, two questions come to mind:
Is it possible to extend $gamma$ on the left
$$tag 1 gamma_{a^♪}: [a^♪,b] to X text{ with } a^♪ lt a text{?}$$
Is it possible to extend $gamma$ on the right
$$tag 2 gamma_{b^♪}: [a,b^♪] to X text{ with } b^♪ gt b text{?}$$
Definition: A metric segment is said to be maximal if it can't be extended.
I googled and searched but didn't find this idea anywhere.
Has this been pursued in any way?
or
Are there related definitions/theories involving metric spaces?
reference-request metric-spaces soft-question definition
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
$endgroup$
Recall the definition of a metric segment in a metric space $(X,d)$.
Using the definition 'setup' from the article, two questions come to mind:
Is it possible to extend $gamma$ on the left
$$tag 1 gamma_{a^♪}: [a^♪,b] to X text{ with } a^♪ lt a text{?}$$
Is it possible to extend $gamma$ on the right
$$tag 2 gamma_{b^♪}: [a,b^♪] to X text{ with } b^♪ gt b text{?}$$
Definition: A metric segment is said to be maximal if it can't be extended.
I googled and searched but didn't find this idea anywhere.
Has this been pursued in any way?
or
Are there related definitions/theories involving metric spaces?
reference-request metric-spaces soft-question definition
reference-request metric-spaces soft-question definition
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
edited Jan 20 at 17:23
CopyPasteIt
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
asked Jan 20 at 17:12
CopyPasteItCopyPasteIt
4,2031628
4,2031628
add a comment |
add a comment |
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