I am looking for results which provides the homology and homotopy groups from some property of the space.
For instance, if a space X is contractible then H_0(X)=\mathbb{Z} and H_n(X)=0 if n\neq 0. Another example is the Eilenberg MacLane spaces K(\pi,n) where \pi_n(K(\pi,n))=\pi and...
Hi everyone,
I have some problems with the pushout construction for Simplicial Sets
The definition of pushouts is as follows:
Let X, Y, Z simplicial sets and f: Z -> X and g: Z -> Y simplicial morphisms, then the pushout is the quotient of the disjoint union of X and Y with the...
I need the demostration of the Taimanov's extension theorem:
This theorem said:
Let A be dense in the T_1-space X. Then in order that a continuos function f from X into a compact space Y have a continuous extension f^*:X\rightarrow Y if and only if that for each two disjoint closed sets F_1...
Definition of simple:
L is called simple if it has no ideals except {0} and L.
I is an ideal of L if x\in L, y\in I \Rightarrow [x,y]\in I
The matrices whose trace is 0 form the special linear lie algebra sl_n(\mathbb{C}). The special linear lie algebra is the lie algebra of the special...