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Metric-spaces
New post in Metric-spaces
Connected sets.
November 11th, 2020
metric-spaces
real-analysis
Check my proof of showing that diam$(A)=$ diam$(\bar{A})$
October 29th, 2020
alternative-proof
proof-verification
metric-spaces
proof-writing
Open set in a metric space is union of closed balls?
August 1st, 2022
metric-spaces
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
June 14th, 2020
inequality
metric-spaces
triangle inequality for a metric space
August 1st, 2022
metric-spaces
general-topology
real-analysis
Why is $\mathbb Q \cap [0,1]$ closed in the rationals?
August 1st, 2022
metric-spaces
real-analysis
Show that every compact subspace of a metric space is bounded in that metric and is closed
August 1st, 2022
metric-spaces
examples-counterexamples
compactness
general-topology
Convergent but not Cauchy under two equivalent metrics
October 16th, 2020
cauchy-sequences
real-analysis
sequences-and-series
metric-spaces
Can an open set contain all of its limit points?
January 3rd, 2020
metric-spaces
real-analysis
general-topology
Lie Derivative of a metric along a vector field
November 13th, 2020
lie-derivative
differential-geometry
metric-spaces
vector-fields
Is any countable set a metric space?
August 1st, 2022
general-topology
metric-spaces
Convergence in $L^\infty$ norm and continuous function
August 1st, 2022
functional-analysis
metric-spaces
convergence-divergence
If $ x $ is a limit point of a Cauchy sequence $ (x_{n})_{n \in \mathbb{N}} $, then $ (x_{n})_{n \in \mathbb{N}} $ converges to $ x $.
August 1st, 2022
real-analysis
general-topology
metric-spaces
Continuity in terms of interior of preimage and preimage of interior
November 12th, 2020
general-topology
metric-spaces
continuity
Distance $D(A, B)$ is defined to be $D(A, B) = \inf d(a, b)$. Show that $D$ does not define a metric on the power set of $X$
April 17th, 2020
metric-spaces
general-topology
real-analysis
Which one of the following subsets of $\Bbb R$ (with the usual metric)is NOT complete?
August 6th, 2020
metric-spaces
d1 and d2 metrics on C[0,1] - topologically inequivalent. Why?
April 30th, 2020
general-topology
metric-spaces
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
August 1st, 2022
metric-spaces
real-analysis
general-topology
Prove that closed and bounded subsets of metric spaces are compact
August 1st, 2022
real-analysis
proof-writing
metric-spaces
proof-verification
general-topology
Example of contraction mapping
February 20th, 2020
fixed-point-theorems
metric-spaces
Is a Baire Space necessarily complete?
August 1st, 2022
metric-spaces
general-topology
real-analysis
baire-category
Difference between open sets and open balls in metric space
August 1st, 2022
metric-spaces
measure-theory
real-analysis
why is any singleton set not open in the set of rational numbers
August 1st, 2022
metric-spaces
infinite subset of discrete metric space is not compact
August 1st, 2022
metric-spaces
compactness
discrete-mathematics
self-learning
Every infinite subset of E in R having a limit point in E implies E is closed and bounded
March 10th, 2020
metric-spaces
general-topology
analysis
How to prove that $|d(x,y)-d(z,w)|\leq |d(x,z)+d(y,w)|$?
August 1st, 2022
inequality
metric-spaces
A sequence in $\mathbb{R}$ that has no Cauchy subsequence
November 24th, 2020
general-topology
cauchy-sequences
real-analysis
sequences-and-series
metric-spaces
$\mathbb{N}$- a complete metric space with $d(x,y)=|x-y|$
August 1st, 2022
metric-spaces
general-topology
Isometric isomorphism between $R^2$ and $R$
June 12th, 2020
metric-spaces
analysis
normed-spaces
isometry
Confusion regarding totally bounded metric spaces having cauchy subsequences of every sequence.
August 1st, 2022
metric-spaces
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