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seen Mar 3 at 19:18

Mar
6
awarded  Yearling
Mar
3
comment Questions about a possible way of representing construcive ordinal numbers
I was trying to work out whether any useful notation systems for a segment of the countable ordinal numbers could be developed, using recursive functions-or even just primitive recursive functions-as the notations. When you pointed out the existence of subsets of K which are densely ordered by "<", I saw what was wrong with this idea and why Hardy (who, I believe, first investigated the ordering "<") never went very far with it.
Mar
2
accepted Questions about a possible way of representing construcive ordinal numbers
Mar
1
comment Questions about a possible way of representing construcive ordinal numbers
Please disregard this last comment
Mar
1
comment Questions about a possible way of representing construcive ordinal numbers
I seem to have lost most of my question
Mar
1
asked Questions about a possible way of representing construcive ordinal numbers
Feb
28
comment A question about open subsets of Hilbert space whose complements are compact sets
V is a G-delta set (an intersection of a countable sequence of open sets). Since you have shown V to be both connected and locally connected, it follows that V is also arc-wise connected.
Feb
27
comment A question about open subsets of Hilbert space whose complements are compact sets
Many thanks for the proof which I was not quite able to find for myself
Feb
27
accepted A question about open subsets of Hilbert space whose complements are compact sets
Feb
26
asked A question about open subsets of Hilbert space whose complements are compact sets
Feb
10
awarded  Good Question
Feb
3
comment Some questions about “inspecting” the boundary of a closed ball in Hilbert space
I see what you are saying. A compact subset of any metric space M, is always a subset of a finite union of arbitrarily small balls of M. If H is the metric space and U is any finite union of sufficiently small balls of H, then it is easy to see that there exist points of S which are not "visible" from any point of U. I was confused by the (irrelevant) fact that-since H is infinite dimensional-no ball of H, however small, can be compact.
Feb
2
comment Some questions about “inspecting” the boundary of a closed ball in Hilbert space
Your nice covering certainly shows that C can be the homeomorphic image of a straight line-which I had thought to be impossible. In fact C can be the homeomorphic image of a ray. You also point out that C must be an infinite set and can be countable. But how, then, to show that C cannot be an infinite compact set, does not seem so obvious-although I think I can see a way.
Feb
1
accepted Some questions about “inspecting” the boundary of a closed ball in Hilbert space
Jan
31
asked Some questions about “inspecting” the boundary of a closed ball in Hilbert space
Dec
11
comment Is a particular type of question about certain infinite sets still being asked?
That's clever and a hard act to follow.
Dec
11
accepted Is a particular type of question about certain infinite sets still being asked?
Dec
11
comment Is a particular type of question about certain infinite sets still being asked?
Many thanks for your responses. I had never heard of any of these examples before.
Dec
7
asked Is a particular type of question about certain infinite sets still being asked?
Nov
8
comment Questions related to a previous question about interpolation based on non-decreasing polynomials
Many thanks, Bjorn, for fixing the mess I made. I was trying to start a new line beginning with several spaces, so that it would look like the start of a new paragraph. Every time I try to do this, I get into trouble.