finite intersection property
... Tn abbreviated f.i.p., if every finite subcollection {A1 , A2 , . . . , An } of A satisifes i=1 Ai 6= ∅. The finite intersection property is most often used to give the following equivalent condition for the compactness of a topological space (a proof of which may be found here): Proposition. A topo ...
... Tn abbreviated f.i.p., if every finite subcollection {A1 , A2 , . . . , An } of A satisifes i=1 Ai 6= ∅. The finite intersection property is most often used to give the following equivalent condition for the compactness of a topological space (a proof of which may be found here): Proposition. A topo ...
What is an Eilenberg-MacLane space?
... A connected, pointed space is called an Eilenberg-MacLane space if it has only one non-trivial homotopy group. It is denoted by K(G, n) where G is the nth homotopy group of the space. As we will see, this notation is well defined since there is only one such space up to homotopy equivalence. Moreove ...
... A connected, pointed space is called an Eilenberg-MacLane space if it has only one non-trivial homotopy group. It is denoted by K(G, n) where G is the nth homotopy group of the space. As we will see, this notation is well defined since there is only one such space up to homotopy equivalence. Moreove ...
Algebraic Topology Introduction
... X/Z. However there is a problem in saying “the” quotient space, as topologizing X/Z depends crucially on the quotient map p : X → Z. I think I was initially confused because there is not a canonical “quotient” in the category of topological spaces, as there is for say, the category of groups or modu ...
... X/Z. However there is a problem in saying “the” quotient space, as topologizing X/Z depends crucially on the quotient map p : X → Z. I think I was initially confused because there is not a canonical “quotient” in the category of topological spaces, as there is for say, the category of groups or modu ...
