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
asked Nov 19 at 9:43
xuq01
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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 Nov 19 at 9:43
xuq01
1012
2
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
Nov 19 at 9:53
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
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
Nov 19 at 12:54
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 Nov 19 at 9:43
xuq01
1012
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 Nov 19 at 9:43
xuq01
1012
asked Nov 19 at 9:43
xuq01
1012
asked Nov 19 at 9:43
xuq01
1012
asked Nov 19 at 9:43
xuq01
1012
asked Nov 19 at 9:43
xuq01
1012
1012
2
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
Nov 19 at 9:53
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
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
Nov 19 at 12:54
add a comment |
2
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
Nov 19 at 9:53
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
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
Nov 19 at 12:54
2
2
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
Nov 19 at 9:53
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
Nov 19 at 9:53
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
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
Nov 19 at 12:54
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
Nov 19 at 12:54
add a comment |
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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
Nov 19 at 9:53
@DaveL.Renfro Want to make this an answer? I will accept it if you do so.
– xuq01
Nov 19 at 10:02
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
Nov 19 at 12:54