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Difference between continuity and uniform continuity
Jan 27, 2014 · I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. …
general topology - Closure of continuous image of closure
Nov 14, 2012 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Proof that the continuous image of a compact set is compact
Take any open cover of F(K), as F is continuous, the inverse images of those open sets form an open cover of K. Since K is compact there is a finite subcover. By construction, the images of …
What's the difference between continuous and piecewise …
Oct 15, 2016 · A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each …
Proving the inverse of a continuous function is also continuous
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · So the right-continuous property has a place of prominence in this fundamental question. This fact is useful to resolve this natural question: Let $\{X_i\}_{i=1}^{\infty}$ be i.i.d. …
finance - Proof of Continuous compounding formula
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 …
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.). …
Prove that the function $\\sqrt x$ is uniformly continuous on …
Nov 17, 2013 · $\begingroup$ @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb{R}$, compact sets are closed …
is bounded linear operator necessarily continuous?
Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider …
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