Which term came first, “open set” or “open interval”?
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As anyone familiar with toplogy may know, open/closed intervals are closely related with open/closed sets in the standard topology on $mathbb{R}$. I am interested in the mathematical history behind this: which term came first historically, "open interval" or "open set"?
general-topology math-history
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As anyone familiar with toplogy may know, open/closed intervals are closely related with open/closed sets in the standard topology on $mathbb{R}$. I am interested in the mathematical history behind this: which term came first historically, "open interval" or "open set"?
general-topology math-history
asked 18 hours ago
xuq01
1012
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xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
As anyone familiar with toplogy may know, open/closed intervals are closely related with open/closed sets in the standard topology on $mathbb{R}$. I am interested in the mathematical history behind this: which term came first historically, "open interval" or "open set"?
general-topology math-history
asked 18 hours ago
xuq01
1012
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
As anyone familiar with toplogy may know, open/closed intervals are closely related with open/closed sets in the standard topology on $mathbb{R}$. I am interested in the mathematical history behind this: which term came first historically, "open interval" or "open set"?
general-topology math-history
general-topology math-history
asked 18 hours ago
xuq01
1012
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
xuq01
1012
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
xuq01
1012
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
xuq01
1012
asked 18 hours ago
xuq01
1012
1012
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
xuq01 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago
add a comment |
1
Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago
1
1
Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago
add a comment |
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1
Open intervals came first, with the more abstract notion of open set not really being a concept people dealt with until roughly the middle of the 1900-1910 decade (and then only occasionally). Prior to this people talked about being in the interior of an interval, with "open interval" and "closed interval" not being a distinction anyone made (in the late 1800s). Sure, people knew the difference between $(a,b)$ and $[a,b],$ but other than saying "endpoints included" and such, they just used the word "interval". See this paper for more.
– Dave L. Renfro
18 hours ago
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
18 hours ago
If no one else says anything I'll do this, maybe after checking on a few things first. I wrote that comment quickly as I was heading out the door earlier this morning, and in 5 minutes I have a Skype meeting, after which I have to leave home for 5-6 hours, so it won't be until several hours before I'd have a chance, and I might just wait until tomorrow morning anyway, when I'll be fresher and not as busy.
– Dave L. Renfro
15 hours ago