|
- Locally compact metric space - Mathematics Stack Exchange
So any incomplete locally compact metric space is a counter-example to "only if" Moreover, as mentioned Tsemo Aristide's answer, any non-compact metric space, even a proper one, has the same topology as some improper metric space
- algebraic geometry - Why is a smooth connected scheme irreducible . . .
More generally, locally with finitely many irreducible components is enough (each point has a neighborhood with finitely many irreducible components) The full statement is then "every regular, connected scheme with locally finitely many irreducible components is irreducible"; which in turn is a particular case of "every connected topological space which has disjoint irreducible components and
- general topology - Rational numbers are not locally compact . . .
Rational numbers are not locally compact Ask Question Asked 6 years, 10 months ago Modified 4 months ago
- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- general topology - Definition of a locally Euclidean space . . .
In general, (Y, σ) (Y, σ) may not have the same "self-similarity" property of Rn R n which makes the two definitions of "locally Euclidean" equivalent So we get two inequivalent candidates for a general notion of "locally homeomorphic" here
- algebraic geometry - Constant sheaf vs locally constant sheaf . . .
Locally constant sheaf Locally constant sheaf: A sheaf F F such that there is an open cover Uα U α of X with F|Uα F | U α is a constant sheaf I know that a constant sheaf is a locally constant sheaf but I don't see why a locally constant sheaf isn't a constant sheaf
- the equivalency of two definitions of locally closed sets
here there are 2 definitions of locally closed sets: A A is locally closed subset of X X if: a) every element in A A has a neighborhood V V in X X such that A ∩ V A ∩ V is closed in V V b) A A is open in its closure (in X X) why a) and b) are equivalent?
|
|
|