generalized intermediate value theorem
The sets and are disjoint open subsets of in the subspace topology, and they are both non-empty, as is contained in one and is contained in the other. If , then constitutes a of the space , contradicting the hypothesis that is the continuous image of the connected space . Thus there must exist such that . ∎
- 1 J. Munkres, Topology, 2nd ed. Prentice Hall, 1975.
|Title||generalized intermediate value theorem|
|Date of creation||2013-03-22 17:17:44|
|Last modified on||2013-03-22 17:17:44|
|Last modified by||azdbacks4234 (14155)|