# topoloogiline ruum

olemus
(i) nii H ise kui ka tühi hulk on lahtised
(ii) mistahes lahtiste hulkade ühend on samuti lahtine hulk
(iii) mistahes kahe lahtise hulga ühisosa on lahtine hulk
=
Merriam-Webster:
: a set with a collection of subsets satisfying the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of any finite number of the subsets is an element of the collection
=
a space which has an associated family of subsets that constitute a topology. The relationships between members of the space are mathematically analogous to those between points in ordinary two- and three-dimensional space.

näide
reaalarvude hulga mingi alamhulk on lahtine,
kui temas on koos iga reaalarvuga r ka
mingi seda reaalarvu sisaldav vahemik (a,b), st a < r < b

ülevaateid
https://i.stack.imgur.com/QNzzA.png

https://christopherolah.files.wordpress.com/2011/04/spaces1.png

https://en.wikipedia.org/wiki/Topological_space

http://mathworld.wolfram.com/TopologicalSpace.html

https://www.encyclopediaofmath.org/index.php/Topological_space

https://www.maths.tcd.ie/~pete/ma2223/chapter2.pdf

https://www.dpmms.cam.ac.uk/~twk/Top.pdf

vt ka
- topoloogia

# topoloogiline ruum

olemus
(i) nii H ise kui ka tühi hulk on lahtised
(ii) mistahes lahtiste hulkade ühend on samuti lahtine hulk
(iii) mistahes kahe lahtise hulga ühisosa on lahtine hulk
=
Merriam-Webster:
: a set with a collection of subsets satisfying the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of any finite number of the subsets is an element of the collection
=
a space which has an associated family of subsets that constitute a topology. The relationships between members of the space are mathematically analogous to those between points in ordinary two- and three-dimensional space.

näide
reaalarvude hulga mingi alamhulk on lahtine,
kui temas on koos iga reaalarvuga r ka
mingi seda reaalarvu sisaldav vahemik (a,b), st a < r < b

ülevaateid
https://i.stack.imgur.com/QNzzA.png

https://christopherolah.files.wordpress.com/2011/04/spaces1.png

https://en.wikipedia.org/wiki/Topological_space

http://mathworld.wolfram.com/TopologicalSpace.html

https://www.encyclopediaofmath.org/index.php/Topological_space

https://www.maths.tcd.ie/~pete/ma2223/chapter2.pdf

https://www.dpmms.cam.ac.uk/~twk/Top.pdf

vt ka
- topoloogia

Palun oodake...

# topoloogiline ruum

olemus
(i) nii H ise kui ka tühi hulk on lahtised
(ii) mistahes lahtiste hulkade ühend on samuti lahtine hulk
(iii) mistahes kahe lahtise hulga ühisosa on lahtine hulk
=
Merriam-Webster:
: a set with a collection of subsets satisfying the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of any finite number of the subsets is an element of the collection
=
a space which has an associated family of subsets that constitute a topology. The relationships between members of the space are mathematically analogous to those between points in ordinary two- and three-dimensional space.

näide
reaalarvude hulga mingi alamhulk on lahtine,
kui temas on koos iga reaalarvuga r ka
mingi seda reaalarvu sisaldav vahemik (a,b), st a < r < b

ülevaateid
https://i.stack.imgur.com/QNzzA.png

https://christopherolah.files.wordpress.com/2011/04/spaces1.png

https://en.wikipedia.org/wiki/Topological_space

http://mathworld.wolfram.com/TopologicalSpace.html

https://www.encyclopediaofmath.org/index.php/Topological_space

https://www.maths.tcd.ie/~pete/ma2223/chapter2.pdf

https://www.dpmms.cam.ac.uk/~twk/Top.pdf

vt ka
- topoloogia

Andmete allalaadimisel või töötlemisel esines tehniline tõrge.
Vabandame!