Recent content by mikeeey

Hi The polynomial ( 1+x^2 ) Can this polynomial span the space of polynomials of degree 2 in standard basis ?

Hi How can i prove that the set if circles does not form a vector space AXIOMATICALLY . ( i am not considering a circle lives in xy-plane ( subset ) as a subspace of xy-plane

Thank you very much , now i understand why we choose functions to relate spaces , and alao i think functions appear in nature of physics a lot ( by means function decribe the nature ) and easy to handle because we know how elements are related .

No , there is no uniqueness A relation which is not function e.g. X^2+Y^2=1 , this is between two sets Now if a set with a structure ( space ) is there relation( not map ) between the two space or groups ? And how would it look like ?

Hello every one . A relation ( is a subset of the cartesian product between Xand Y) in math between two sets has spatial types 1-left unique ( injective) 2- right unique ( functional ) 3- left total 4- right total (surjective) May question is 1- a function ( map...

My friend , i study advanced mathematics , but i saw a video speaks about the meaningless spacetime in sigularity point where things start breaking down of the concepts , i will change my phrase [ what happens to that instantaneous singilarity point (where all infinite densed matter lives in it...

Hello every one . Simple question , What happens to the ended spacetime fabric in the singularity poing of the black hole if the black hole starts to move in spacetime ? Would the dead spacetime fabric at that point return to the regular shape of space time fabric ? ( as we know spacetime at...

This is the problem ,its the same as GR issue , it's like how to solve einstein's field equations , how to set the coordinate chart without knowing how the lorentzian manifold would look like , the only way to solve then by using assumptions for some famous topological spaces like the...

Sorry i meant how to visualize the manifold in order to draw the chart ! By taking the coordinates limits , a manifold can be covered by a single chart like Earth single atlas or by multi charts

There is no such thing called drawing in higher dimensional manifold, u can not visualized it to draw it ! , its only inserting some prodicting chart ! , E.g. Consider the black hole by schwarzschild solution , how the manifold would be taken to be ?! In wikipedia the manifold would considered...

But u can't imagine a 3- spatial manifold ! How can one chart it ?! As i said in GR , u have the equations , in order to solve u need to know how the manifold looks like to u use charting map and base u r equations on the chart !

Hi How can a person chart a manifold if he does not know how the manifold looks like ? E.g. The 2-sphere manifold can have 2 charts and symmetric charts with the chart goes like this ( theta from zero to pi , psy from minus pi to pi ) but the problem for unknown manifold , e.g. In general...

Hi All A mathematical structure : is A set with an Object ( structure ) and there are generally two types of mathematical structure , which are algebraic structure and space ( geometric structure ) Eaxmples of algebraic structure are rings , fields , modules vector spaces ... act Examples of...

Thank you

Last question , how does the curvature tensor of the surface of the sphere is not zero and still locally flat ?! Thanks