Recent content by Streltsy

Which of your claims should I still consider? (With all due respect).

With respect to the continuity of f; doesn't the fact that f: S1 \ {(0,1)} → ℝ safeguard against discontinuity? The domain of f does not include y = 1 so, from my understanding, f-1 ° f would be defined everywhere in the domain of f. Still, I suppose I have to arrive at the definition of...

Sorry, I haven't gotten to the definition of compactness. Although I believe I understand why my assumption is wrong. I have another question; though I'm not sure if it would belong in this section. Suppose I have a function f(x,y) = 2x/(1-y), that maps the sphere (minus a pole), S1 = {(x...

Given this definition of two homeomorphic spaces, Definition 1.7.2. Two topological spaces X and Y are said to be homeomorphic if there are continuous map f : X → Y and g : Y → X such that f ° g = IY and g ° f = IX. Suppose I know f and g are both continuous. Would it be safe to assume...

Thank you guys.

Oh ok. Would it be safe to say, then, that d(f, g) =max|f − g| does not define a metric on X for this particular case, because X is a set of functions that map [0,1] to R, and R is unbounded? So one might be able to prove that "if d(f, g) =max|f − g| = 0, then f = g", but not the converse...

Technically, this is not a homework question, since I solely seek an answer for self-indulgence. Homework Statement Example 1.1.4. Suppose f and g are functions in a space X = {f : [0, 1] → R}. Does d(f, g) =max|f − g| define a metric? Homework Equations (1) d(x, y) ≥ 0 for all x, y...