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Mozibur Ullah
Mozibur Ullah
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I answered this question on "is there a longest geodesic" by a kind of a joke, which I couldn't resist: the long line! It wasSimply going by the name it had to be the 'longest geodesic'! I didn't bother explaining the joke, after all, a joke that requires explaining, is no joke at all, in my exoerience.

I cinsidered it a joke because I didn't know of a theory of such 'large' manifolds and I thought my intentions wpuldwould be clear - they weren't apparently.

But then, much to my surprise, whilst researching something else entirely, I I came upon a classification of such 'large' surfaces! Unfortunately I didn't make a note of it. However, whilst trying to find where and what this result exactly is, I came upon a paper by Rafael Dahmen on embeddings of the long line in weakly complete vector spaces. These are spaces like $R^I$ for arbitrary $$. The paper is here and titled: Smooth Embeddings of the Long Line and other Non-Paracompact Manifolds into Locally Convex Spaces.

Q. What I'm after is a paper or a book outlining the clasdifyingclassification of such large surfaces.

I recall the source that I had looked at said it was summarising the findings ofreferenced a certain book, a handbook, from what I recall. Unfortunately Unfortunately, I don't remember the title of the book or which spurcesource it was - other than the source was online. Hence the question.

I answered this question on "is there a longest geodesic" by a kind of a joke, which I couldn't resist: the long line! It was a joke because I didn't know of a theory of such 'large' manifolds and I thought my intentions wpuld be clear - they weren't apparently.

But then, much to my surprise, whilst researching something else, I came upon a classification of such 'large' surfaces! Unfortunately I didn't make a note of it. However, whilst trying to find where and what this result exactly is, I came upon a paper by Rafael Dahmen on embeddings of the long line in weakly complete vector spaces. These are spaces like $R^I$ for arbitrary $$. The paper is here and titled: Smooth Embeddings of the Long Line and other Non-Paracompact Manifolds into Locally Convex Spaces.

Q. What I'm after is a paper or a book outlining the clasdifying such large surfaces.

I recall the source that I had looked at said it was summarising the findings of a certain book. Unfortunately, I don't remember the title of the book or which spurce it was - other than the source was online.

I answered this question on "is there a longest geodesic" by a kind of a joke, which I couldn't resist: the long line! Simply going by the name it had to be the 'longest geodesic'! I didn't bother explaining the joke, after all, a joke that requires explaining, is no joke at all, in my exoerience.

I cinsidered it a joke because I didn't know of a theory of such 'large' manifolds and I thought my intentions would be clear - they weren't apparently.

But then, much to my surprise, whilst researching something else entirely, I came upon a classification of such 'large' surfaces! Unfortunately I didn't make a note of it. However, whilst trying to find where and what this result exactly is, I came upon a paper by Rafael Dahmen on embeddings of the long line in weakly complete vector spaces. These are spaces like $R^I$ for arbitrary $$. The paper is here and titled: Smooth Embeddings of the Long Line and other Non-Paracompact Manifolds into Locally Convex Spaces.

Q. What I'm after is a paper or a book outlining the classification of such large surfaces.

I recall the source that I referenced a certain book, a handbook, from what I recall. Unfortunately, I don't remember the title of the book or which source it was - other than the source was online. Hence the question.

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Mozibur Ullah
Mozibur Ullah
  • 2.4k
  • 15
  • 21

What 'large' surfaces are there?

I answered this question on "is there a longest geodesic" by a kind of a joke, which I couldn't resist: the long line! It was a joke because I didn't know of a theory of such 'large' manifolds and I thought my intentions wpuld be clear - they weren't apparently.

But then, much to my surprise, whilst researching something else, I came upon a classification of such 'large' surfaces! Unfortunately I didn't make a note of it. However, whilst trying to find where and what this result exactly is, I came upon a paper by Rafael Dahmen on embeddings of the long line in weakly complete vector spaces. These are spaces like $R^I$ for arbitrary $$. The paper is here and titled: Smooth Embeddings of the Long Line and other Non-Paracompact Manifolds into Locally Convex Spaces.

Q. What I'm after is a paper or a book outlining the clasdifying such large surfaces.

I recall the source that I had looked at said it was summarising the findings of a certain book. Unfortunately, I don't remember the title of the book or which spurce it was - other than the source was online.