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- Proof of Continuous compounding formula - Mathematics Stack Exchange
Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a
- Closure of continuous image of closure - Mathematics Stack Exchange
Closure of continuous image of closure Ask Question Asked 12 years, 8 months ago Modified 12 years, 8 months ago
- Proving the inverse of a continuous function is also continuous
6 All metric spaces are Hausdorff Given a continuous bijection between a compact space and a Hausdorff space the map is a homeomorphism Proof: We show that f f is a closed map Let K ⊂E1 K ⊂ E 1 be closed then it is compact so f(K) f (K) is compact and compact subsets of Hausdorff spaces are closed Hence, we have that f f is a homeomorphism
- Topological properties preserved by continuous maps
You'll find topological properties with indication of whether they are preserved by (various kinds of) continuous maps or not (such as open maps, closed maps, quotient maps, perfect maps, etc ) For mere continuous most things have been mentioned: simple covering properties (variations on compactness, connectedness, Lindelöf) and separability
- real analysis - Continuous mapping on a compact metric space is . . .
I am struggling with this question: Prove or give a counterexample: If f: X → Y f: X → Y is a continuous mapping from a compact metric space X X, then f f is uniformly continuous on X X Thanks for your help in advance
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