ChatGPT for Analysis Point Set Topology, Rn Convergence, Euclidean and Metric Spaces

Feature added May 31, 2023:
These links contain the questions and the answers:

Point-set topology:
difference between an arbitrary and a finite collection of subsets in point-set topology
open and closed balls in point-set topology
relatively open and closed sets examples
difference between relatively open and open with examples
define connectivity
define limit point
an example of a limit point
when does a set not contain at least one limit point
define compact set
examples of compact sets
define the Heine-Borel Theorem
define compact subsets of Euclidean spaces with examples
example of a cover and subcover for [0,1]
examples of why there are no covers or subcovers of (0,1)
relatioship between compact sets and connected sets

R(n) Convergence:
define separable set
example of a separable set in rationals
define algebraic numbers with examples
a nondegenerate interval cannot have measure zero with examples
example of a closed interval on the real line with measure zero
example of a reimann integrable function with countably many points of discontinuity
define the closed graph theorem in analysis
examples of limits of sequence points in R^n
is the empty set a compact set

Euclidean and Metric Spaces:
definition of a directed line segment in R^n
definition of a hyperplane in vector analysis
define affine subspace
define subspace codimension
define linear operator
examples of linear operators
define topology
difference between Euclidean norm, L-one-norm, and sup-norm with examples
sets both open and closed in R(n)
define the discrete space R
define the set of real numbers equipped with the discrete topology
examples of spaces that are not metric spaces
difference between open and closed sets to describe covergence of sequences in an arbitrary metric space
define cluster point with examples
is every point in a metric space either an isolated point or a cluster point

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All of the chatbots videos can be found here:
If you can think of a better way to engage with chatbots for mathematics, please leave a comment!
These videos are on a tangent to the other content in this channel:
Playlist for Math Books Read or Collected here:

[mathematicaladventures]

All of the chatbots videos can be found here:
If you can think of a better way to engage with chatbots for mathematics, please leave a comment!
These videos are on a tangent to the other content in this channel:
Playlist for Math Books Read or Collected here: