Notation for the set $\{[x, \infty) : x \in \mathbb{R}\}$?

Asked Jul 16 '24 at 00:30

Active Jul 16 '24 at 04:22

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Is there a special notation for the set $\{[x, \infty) : x \in \mathbb{R}\}$? This is, the set of all connected subsets of $\mathbb{R}$ that have a minimum element and no supremum.

(Incidentally, this is the set of all filters of the lattice $(\mathbb{R}, \max, \min))$.

edited Jul 16 '24 at 04:22

Anne Bauval

49,005

asked Jul 16 '24 at 00:30

lafinur

3,783

1

Why is this being downvoted? The question is similar to, for example, this well-received question: https://math.stackexchange.com/questions/55591/notation-for-the-set-of-all-finite-subsets-of-mathbbn – lafinur Jul 16 '24 at 00:52
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That question is from 12 years ago. Standards have changed a lot since then. – JonathanZ Jul 16 '24 at 01:18
What is a continuous subset? Do you mean a connected subset? – Malady Jul 16 '24 at 01:38
Continuity is about functions, not sets. What do you mean by continuous subsets? – Thomas Andrews Jul 16 '24 at 01:45
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Also, $(x,+\infty)$ is a filter on that lattice, too. – Thomas Andrews Jul 16 '24 at 01:47
It was connected, my mistake. Fixed it. – lafinur Jul 16 '24 at 02:16
To my knowledge there isn’t. – Iq-n-dI Jul 16 '24 at 05:31
It's the image of $\mathbb{R}$ under the $(0, 1)$-Yoneda embedding, so you could be tongue-in-cheek and write $よ(\mathbb{R})$. – Naïm Camille Favier Jul 16 '24 at 08:21

Notation for the set $\{[x, \infty) : x \in \mathbb{R}\}$?

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