Timeline for When is a distance space dominated by a metric space?

9 events

when toggle format	what		by	license	comment
S Feb 9 at 19:48	history	suggested	Paul Tupper	CC BY-SA 4.0	changed "those these" to "but these"
Feb 9 at 17:14	review	Suggested edits
S Feb 9 at 19:48
Feb 8 at 19:12	comment	added	YCor		Just a comment on the last example ($(X,\delta)$ any infinite compact metric space with $d(x,y)=1/\delta(x,y)$ for $x\neq y$): every uncountable metric space has an finite (and even uncountable) bounded subspace. In this example, every infinite subset has an accumulation point, which means has pair of points for which the function $d$ tends to infinity, so cannot be bounded for any distance $\ge d$.
Feb 8 at 18:45	history	edited	David Bryant	CC BY-SA 4.0	Fixed notation for the reals.
Feb 8 at 17:44	comment	added	Peter LeFanu Lumsdaine		@YCor: Agreed, though it’s not absolutely nonexistent — I remember seeing it in some old-ish books (~60s or earlier), I think possibly in set theory?
Feb 8 at 17:38	comment	added	YCor		Your notation $\Re$ is very unusual (it sometimes means real part, but not the set of reals). You probably mean $\mathbf{R}$ or $\mathbb{R}$.
Feb 8 at 17:33	history	edited	David Bryant	CC BY-SA 4.0	Added additional information
Feb 8 at 16:18	comment	added	YCor		If $X$ is countable this is easy by induction. Namely $X=\{x_i:i\ge 0\}$, $x_i$ distinct, and define $\rho(x_i,x_j)=u_j$ for $i<j$ with $u_j$ increasing, and large enough (namely $\ge \max_{i:i<j} d(x_i,x_j)$).
Feb 8 at 3:47	history	asked	David Bryant	CC BY-SA 4.0