matness
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In Hartshorne's book definiton of a dimension is given as follows:
İf X is a t.s. , dim(X) is the supremum of the integers n s.t. there exist a chain
Z_0 \subsetneq Z_1...\subsetneq Z_n
of distinct irreducible closed subsets of X
My question is:
Can we conclude directly that any topological space has dim greater than or equal to 1, since empty set and and X itself is always closed?
Example in the same book says no in a way.It says A^1 has dim 1.
Although \emptyset \subsetneq {any point} \subsetneq X
Should I exclude empty set ?
İf X is a t.s. , dim(X) is the supremum of the integers n s.t. there exist a chain
Z_0 \subsetneq Z_1...\subsetneq Z_n
of distinct irreducible closed subsets of X
My question is:
Can we conclude directly that any topological space has dim greater than or equal to 1, since empty set and and X itself is always closed?
Example in the same book says no in a way.It says A^1 has dim 1.
Although \emptyset \subsetneq {any point} \subsetneq X
Should I exclude empty set ?