اريد تعريف واضح ومثال عن................

nabihalia84

nabihalia84

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اريد تعريف واضح ومثال عن(( manifold in topology ))واذا كان ممكن ان تكون المساعده باللغه الانجليزيه
;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(
والموضوع مهم جدااااااااااااااااااااااااااااااااااااااااااااا ارجو المساعدة​
 


nabihalia84 قال:
اريد تعريف واضح ومثال عن(( manifold in topology ))واذا كان ممكن ان تكون المساعده باللغه الانجليزيه

;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(

والموضوع مهم جدااااااااااااااااااااااااااااااااااااااااااااا ارجو المساعدة​
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اخي العزيز ارجو ان يفيدك هذا الكتاب

Introduction to Topological Manifolds (Graduate Texts in Mathematics)


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http://mihd.net/zyk9fd/__3425fb7__via_gigapedia.info__.html

او

http://rapidshare.com/files/76572871/0387950265.pdf.zip
 


شكراااااااااااااااااااااااااااااااااااااااااااااااااااااااا
:clap:(talk):clap:
قد افادنى الكتاب كثيراااااااااااااااااااااااااااااااااا
:):)
 


nabihalia84 قال:
اريد تعريف واضح ومثال عن(( manifold in topology ))واذا كان ممكن ان تكون المساعده باللغه الانجليزيه​


;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(;(​

والموضوع مهم جدااااااااااااااااااااااااااااااااااااااااااااا ارجو المساعدة​
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Manifold in Topology
In mathematics, a topological manifold is a Hausdorfftopological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout mathematics.
A manifold can mean a topological manifold, or more frequently, a topological manifold together with some additional structure. Differentiable manifolds, for example, are topological manifolds equipped with a differential structure. Every manifold has an underlying topological manifold, obtained simply by forgetting the additional structure. An overview of the manifold concept is given in that article. This article focuses purely on the topological aspects of manifolds.​


Contents​

 


شكرااااااااااااااااااااااااااااااااااااااااااااااااااااااااااااااااااااا(party)
لو كنت اعرف ان المساعده بها الشكل كنت طلبتها من زمان
بس اتحملونى لان عندى طلبات كثيررررررررررررررررره(blush)
وشكراااااااااااااااااااااااااااااااااااااااااااااااااااااا:*
والله خجلتونى(wasntme)(wasntme)
 


السلام عليكم أشكركم على الاجابة على هذا الموضوع لأنه من أهم الدروس في الرياضيات البحتة :clap: مشكوريييييييييييييييييييييييييييييييييييييييييين
 
Please excuse my English, (blush) (ça aurait été mieux si tu avais demandé ça en Français!!! :D )
Please allow me to give you a definition somewhat more "physical": 8-|
We are living in a "round planet", (hi) but we see all around us flat surfaces |(, this is in fact because we can look only in our neighborhood! So, locally, our planet is flat, mathematically, one says that the sphere is locally like "R2".8-|

Frequently, we need to assign to points of our space coordinates, and one wishes for these coordinates to be in a one to one correspondence with points, this can never be the case in a sphere (sweat) , thus we need to compare our sphere with "R2" in which a coordinates system is well implemented (party) , this can be done using a "HOMEOMORPHISM" |-) , roughly speaking, it is a transformation that deforms CONTINUOUSLY a space into another space (mathematically it is a bi-continuous bijection 8-| ), but we have a problem, one cannot deform continuously a sphere into R2 :rain: ! we need to choose "patches" that can be deformed into R2, a necessary condition is the 2by2 overlapping of these "patches" that we call "charts", the simplest choice for our sphere is to take 2 charts :eek: , the first one is the whole sphere MINUS the "north pole" and the second is the whole sphere MINUS the "South Pole", these charts have an overlapping that is the whole sphere MINUS the "north pole+South Pole", and these two patches can be CONTINUOUSLY DEFORMED INTO R2 (party) :clap: each one, then we can define a system of coordinates in each of them by taking the inverse image of the coordinates on R2 by the inverse homeomorphism, it remains to define a consistency condition on the two kinds of coordinates that has a point that is on the overlapping of two patches |-) , the transformation that bring us from the first system of coordinates into the second must be differentiable and continuous. (wait)

Hope that I had illuminate you :D :handshake: :eek: (hi)
 


i ask about the deffinition of a manifold but when i read your answer i
found nothing about my question and any way thankssssssssssss
:*:*:*:*:*:*:*:*:*:*:* :*:*:*:*:*
and thank you so mush four your intresting
 


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