Intereting Posts

Can you prove the following formula for hypergeometric functions?
Is the outer boundary of a connected compact subset of $\mathbb{R}^2$ an image of $S^{1}$?
The resemblance between Mordell's theorem and Dirichlet's unit theorem
Generalisation of alternating functions
Finding Sylow 2-subgroups of the dihedral group $D_n$
Method to find $\sin (2\pi/7)$
Singular measures on Real line
What is the name of the logical puzzle, where one always lies and another always tells the truth?
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
Are $R=K/(ad-bc, a^2c-b^3, bd^2-c^3, ac^2-b^2d)$ and $K$ isomorphic?
Ways to induce a topology on power set?
Two definitions of tensor product: when are they equivalent?
Determine the center of the dihedral group of order 12
Conjectured primality test
Solve $x^2+2=y^3$ using infinite descent?

Can anybody suggest me a good book on Metric Spaces. Although I am not new to this subject, but want to polish my knowledge. I want a book which can clearly clear my basics. I want to start from the basics. Kindly suggest me. Thanks a lot.

- Metric is continuous function
- Isomorphism isometries between finite subsets , implies isomorphism isometry between compact metric spaces
- Intermediate Text in Combinatorics?
- What's wrong with this definition of continuity?
- When is a metric space Euclidean, without referring to $\mathbb R^n$?
- Distribution theory book
- Complex Analysis Book
- Is there always an equivalent metric which is not complete?
- Distances between closed sets on metric spaces
- How to show $d(x,A)=0$ iff $x$ is in the closure of $A$?

- Copson E.T. Metric spaces. Cambridge University Press, London, 1968. v+143 pp.
- Kaplansky I. Set theory and metric spaces. Chelsea Publishing Co., New York, 1977. xii+140 pp.
- Searcóid M.Ó. Metric spaces. Springer-Verlag, London, 2007. xx+304 pp.

I suggest Topology of Metric Spaces by s. Kumaresan.

**In the preface:**

The aim is to give a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete

spaces and geometric ideas. To encourage the geometric thinking, I have

chosen large number of examples which allow us to draw pictures and

develop our intuition and draw conclusions, generate ideas for proofs.

To this end, the book boasts of a lot of pictures. A secondary aim is

to treat this as a preparatory ground for a general topology course and

arm the reader with a repertory of examples.

I suggest “Introductory Functional Analysis With Applications” By “Erwin Kreyszig”. Its 1st Chapter gives a very nice introduction to Metric Spaces… Good Luck

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- finding a minorant to $(\sqrt{k+1} – \sqrt{k})$
- Linear Algebra: determine whether the sets span the same subspace
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- Transient diffusion with compact support throughout (not just initially)
- Does $\sin n$ have a maximum value for natural number $n$?