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visits | member for | 5 years, 1 month |
seen | Mar 3 at 19:18 | |
stats | profile views | 1,635 |
Apr 4 |
awarded | Popular Question |
Mar 6 |
awarded | Yearling |
Mar 3 |
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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 |
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Questions about a possible way of representing construcive ordinal numbers
Please disregard this last comment |
Mar 1 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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? |