Post History
#2: Post edited
by
Guilherme Gondin
·
2021-12-31T19:18:56Z (almost 3 years ago)
- First a very important side note, by the chaos period set theory, mathematical logic and all the modern theory of mathematic foundation was happening.
- With this in mind, by ???, more specificaly in 1914, Hausdorff published a book called Principles of Set Theory,one of the most important books in the history of mathematics, in this book, while researching how set theory could formalize what were know by the time about analysis, Hausdorff used the idea of neighborhood, that were already know to be a valid idea in all approachs of analysis yet studied,for defining the now standard axioms for a topological space, but including the separation axiom as an axiom for any topological spaces.
Not much latter mathematicians realized that removing the separation axiom, now know as the Hausdorff axiom, whould be a good idea, not only because this way the notion of topological space includes more spaces, but also because some important properties of real analysis do not hold for Hausdorff spaces alone, but do hold for the more abstract notion tological space defined by the other axioms without the separation axiom.
- First a very important side note, by the chaos period set theory, mathematical logic and all the modern theory of mathematic foundation was happening.
- With this in mind, by ???, more specificaly in 1914, Hausdorff published a book called Principles of Set Theory,one of the most important books in the history of mathematics, in this book, while researching how set theory could formalize what were know by the time about analysis, Hausdorff used the idea of neighborhood, that were already know to be a valid idea in all approachs of analysis yet studied,for defining the now standard axioms for a topological space, but including the separation axiom as an axiom for any topological spaces.
- Not much latter mathematicians realized that removing the separation axiom, now know as the Hausdorff axiom, whould be a good idea, not only because this way the notion of topological space includes more spaces, but also because some important properties of real analysis do not hold for Hausdorff spaces alone, but do hold for the more abstract notion tological space defined by the other axioms without the separation axiom.
- Edit: A correction, Hausdorff created an equivalent definition of the modern one, but not the actual modern definition, he defined a topological space by neighbours of points, the current definition was given by Alexandrov in 1925.
#1: Initial revision
by
Guilherme Gondin
·
2021-12-31T17:19:42Z (almost 3 years ago)
First a very important side note, by the chaos period set theory, mathematical logic and all the modern theory of mathematic foundation was happening. With this in mind, by ???, more specificaly in 1914, Hausdorff published a book called Principles of Set Theory,one of the most important books in the history of mathematics, in this book, while researching how set theory could formalize what were know by the time about analysis, Hausdorff used the idea of neighborhood, that were already know to be a valid idea in all approachs of analysis yet studied,for defining the now standard axioms for a topological space, but including the separation axiom as an axiom for any topological spaces. Not much latter mathematicians realized that removing the separation axiom, now know as the Hausdorff axiom, whould be a good idea, not only because this way the notion of topological space includes more spaces, but also because some important properties of real analysis do not hold for Hausdorff spaces alone, but do hold for the more abstract notion tological space defined by the other axioms without the separation axiom.