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May
26
answered The sum of an uncountable number of positive numbers
Sep
24
awarded  Autobiographer
Sep
13
answered $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
Aug
21
accepted How to define $a^x$?
Aug
21
asked How to define $a^x$?
Aug
20
comment Is $\{x\}$ a neighbourhood of $x$?
That depend on our topology. I think you're studying metric spaces only. If you don't know general topology it doesn't matter. Actually by a topology we mean we first set the open sets. I mean we just define that these are the open sets and do maths on that. So you can define a topology on a set in which one particular singleton set is open another one is not open, like that.. So {a} is open in your topology iff {a} is a neighborhood of a. As other people have already mentioned, there is a topology called discrete topo. in which all singleton sets are open. => {x} is a nbd of x for all x..!:)
Aug
20
comment Is $\{x\}$ a neighbourhood of $x$?
Any open set containing our point 'x' is a neighborhood of x. Don't confuse with the real life meaning of 'neighborhoods'. It has no connection with saying that points in a neighborhood of x are closer to x or things like that. Even the whole space itself is a neighborhood of any point!
Aug
20
answered Sphere-sphere intersection is not a surface
Aug
20
answered Show that following subset of $\mathbb R^2$ is compact
Aug
17
answered Prove that invertible metrices set is an open set in a given space, and the determinant is continuous
Aug
17
answered Basic compactness
Aug
17
awarded  Teacher
Aug
17
answered How does one represent a range like $[a,b]$ if the ^range^ is exactly $1$?
Aug
16
awarded  Editor
Aug
16
revised When discussing compactness, is it necessary to specify the metric space?
added 335 characters in body
Aug
16
answered When discussing compactness, is it necessary to specify the metric space?
Mar
17
awarded  Supporter
Mar
17
asked Can we generalize the result of Urysohn's lemma to countable collection of pairwise disjoint closed subsets of a normal space..?
Mar
17
awarded  Scholar
Mar
17
accepted Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..?