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1d
comment Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$
@AshokVardhan try two sequences that alternate between two values
Aug
26
comment topology (upper limit and lower limit)
@user262860 Yes, but none contains $0$. A set $O$ is open iff for every point $p$ in $O$, there is some basic open set of the form $(a,b]$ that contains $p$ and is contained in $O$. Which fails for $0$ only in the case of $[0,1)$.
Aug
26
answered topology (upper limit and lower limit)
Aug
22
answered Intersection of arbitrary union of compact subsets.
Aug
15
answered Point about the theorem and proof of the inner product being a continuous function.
Jul
19
awarded  Enlightened
Jul
19
awarded  Nice Answer
Jul
8
comment How to construct a point finite open cover of $\mathbb{R}$ that is everywhere non-locally finite?
It is a good example, but somewhat overkill. To get a cover that is not locally finite, to fail it at one point is enough.
Jul
8
answered How to construct a point finite open cover of $\mathbb{R}$ that is everywhere non-locally finite?
Jul
8
comment Locally compact spaces that are not first-countable and continuity of functions on locally compact groups and continuity of group representation
As to 1): any uncountable product of compact topological groups, like $\{0,1\}^I$ with uncountable $I$, is such an example. And yes, Lie groups are first countable, as this is a local property.
Jul
7
comment A real function on a compact set is continuous if and only if its graph is compact
@Zhanxiong Because $X \times Y$ has the so-called product topology which is defined as to make projections continuous.
Jul
6
answered How to negate: not a limit point (symbolic logic)
Jul
1
awarded  elementary-set-theory
Jun
30
answered Relationship between completeness and well ordering (meta).
Jun
30
answered Problem on elementary logic and set theory
Jun
29
answered How do I find the type of relation on an infinite set?
Jun
28
comment Weakening compactness in metric spaces
What is "the cardinaility of a net"? That of its domain or its image?
Jun
28
comment Can we define $ℝ^A$ where A is uncountable?
@AsafKaragila only if the domain is well-ordered I would use sequence.
Jun
28
answered Contraction on a metric.
Jun
20
answered Prove $((A^C \cup B^C) \setminus A)^C = A$