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 Enlightened
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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 $((A^C \cup B^C) \setminus A)^C = A$
Jun
7
answered unclear why subset of a lexicographic ordered set of strings is said NOT to have a least element.
Jun
7
comment Generalization of metric spaces?
@StanCoreyCarter You're welcome!
Jun
7
answered Some basic set theory proofs.
Jun
7
revised Prove that sets being equipotent is an equivalence relation
tags, terminology, grammar
Jun
7
answered Generalization of metric spaces?