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hausdorff_space [2014/10/25 16:01] nikolaj |
hausdorff_space [2014/10/25 16:07] nikolaj |
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| | @#FFBB00: definiendum | @#FFBB00: $\langle X,\mathcal{T}_X\rangle \in\mathrm{it} $ | | | @#FFBB00: definiendum | @#FFBB00: $\langle X,\mathcal{T}_X\rangle \in\mathrm{it} $ | | ||
| | @#AAFFAA: inclusion | @#AAFFAA: $\langle X,\mathcal{T}_X\rangle$ ... topological space | | | @#AAFFAA: inclusion | @#AAFFAA: $\langle X,\mathcal{T}_X\rangle$ ... topological space | | ||
| - | | @#DDDDDD: range | @#DDDDDD: $x,y\in X, x\ne y$ | | + | | @#FFFDDD: for all | @#FFFDDD: $x,y\in X, x\ne y$ | |
| - | | @#DDDDDD: range | @#DDDDDD: $U_x\in$ Neighbourhood $x$, $V_y\in$ Neighbourhood $y$ | | + | | @#FFFDDD: exists | @#FFFDDD: $U_x\in$ Neighbourhood$(\mathcal{T}_X,x)$, $V_y\in$ Neighbourhood $(\mathcal{T}_X,y)$ | |
| - | | @#FFFDDD: for all | @#FFFDDD: $x,y$ | | + | |
| - | | @#FFFDDD: exists | @#FFFDDD: $U_x, V_y$ | | + | |
| | @#55EE55: postulate | @#55EE55: $U_x\cap V_y=\emptyset$ | | | @#55EE55: postulate | @#55EE55: $U_x\cap V_y=\emptyset$ | | ||
