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14h
comment General topological space $2$.
@JKnecht Because e.g. $B = [0, \frac{1}{2}] \cap A$, the intersection of a closed set in the ambient space, with $A$
14h
comment Cluster points and the sequence 1,1,2,1,2,3,1,2,3,4,1,…
Better is, "consisting of an infinite subsequence of those rationals", I think.
14h
comment Product topology and projection mappings.
If I understand you correctly, yes. $p_1^{-1}[U]$ is all pairs $(x,y)$ with $x \in U$ and no condition on $y$, hence the intersection with the other set.
19h
comment subset of a complete space has a relatively compact $\varepsilon$-net.
What is a "relatively compact set"? One with compact closure (terminology differs). And a relatively compact "net" is a subset that is relatively compact in this (to be defined) sense, and that is a traditional $\varepsilon$-net, I suppose? Has compact = sequentially compact etc. been studied before?
19h
revised subset of a complete space has a relatively compact $\varepsilon$-net.
edited tags
19h
answered Product topology and projection mappings.
19h
revised Product topology and projection mappings.
LateX
1d
comment Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
Modified formula to be more standard.
1d
revised Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
added 13 characters in body
1d
revised Prove that $(A \cup B)\setminus B=A$ if and only if $A$ and $B$ are disjoint.
added 18 characters in body; edited title
1d
comment Relations between cluster points of nets and types of accumulation points of sets
Problem is, that for uncountable image sets there are very many index sets and nets that will have the same range. The range is way too coarse compared to the net structure (which includes the order on the index set!). What kind of result are you aiming for?
1d
comment Proof of $\aleph_0^{\aleph_0} = \mathbb{c}$ without using Cantor's $2^{\aleph_0} = \mathbb{c}$
This shows that there is an injection from $\mathbb{N}^\mathbb{N}$ into the reals. And equality?
1d
comment Find GCD of polynomials over GF(101)
Do you know how to add, subtract, multiply and divide in $GF(101)$? If you know that, proceed like you would in the reals. There really is no algorithmic difference.
2d
comment Prob. 10 (d), Sec. 19 in Munkres' TOPOLOGY, 2nd ed: How to show that this map is open?
Show $f \left[\cap_{i=1}^n f_{\alpha_i}^{-1}[U_{\alpha_i}] \right]$ is exactly the product set (with the other $U_\alpha = X_\alpha$) intersected with $Z$. Then $f$ is open in base elements and so open for all, as images preserve unions.
2d
comment Prob. 10 (d), Sec. 19 in Munkres' TOPOLOGY, 2nd ed: How to show that this map is open?
(b) is false as stated, you only have a subbase. You need to add finite intersections of those sets to get a base.
2d
comment Decode the text using a 3×3 Hill Cipher
Try "theintern" at all positions (start at the beginning), and solve for the matrix (nine equations, nine unknowns), and decrypt the rest to see if it makes sense. If it fails, try another position. Use a program.
Feb
3
comment Covering maps are proper?
You show that $p^{-1}[K]$ is compact for compact $K$, which is what follows from closedness and compact fibres
Feb
2
comment Covering maps are proper?
You know that if $p$ is closed, continuous and has compact fibres, then $p$ preserves inverse compactness? It's pretty easy to see that finite fibres on a covering map makes $p$ closed, (and fibres compact) so then you're done. See part of the argument in at.yorku.ca/cgi-bin/… for more details.
Feb
2
comment Covering maps are proper?
You're assuming everything is metric (or at least that compact and sequentially compact are the same). You could give a more general proof without sequences.
Feb
2
revised Involutary Keys for Shift Cipher
edited body