Metric Space | Metric Space - Definition , Concept & Examples

📒⏩Comment Below If This Video Helped You 💯
Like 👍 & Share With Your Classmates - ALL THE BEST 🔥

This video lecture on Metric Space | Metric Space - Definition , Concept & Examples | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. What is Metric?
2. What is Metric Space?
3. Definition Of Metric Space and Examples Of Metric Space.
4. This helpful For CSIR NET, IIT-JAM, GATE Exams.
#MetricSpace #MetricSpaceDefinition #ShortTrick #EngineeringMahemaics #BSCMaths #GATE #IITJAM #CSIRNET
This Concept is very important in Engineering & Basic Science Students. This video is very useful for B.Sc./B.Tech & M.Sc./M.Tech. students also preparing for NET, GATE, and IIT-JAM Aspirants.
Find Online Solutions Of Metric Space | Metric Space - Definition, Concept & Examples By GP Sir (Gajendra Purohit)Do Like & Share this Video with your Friends. If you are watching for the first time then Subscribe to our Channel and stay updated for more videos around Mathematics

Time Stamps
0:00 | An Intro.
00:47 | Definition Of Metric Space
03:26 | Example 1 of Metric Space
07:15 | Example 2 of Metric Space
10:28 | Example 3 of Metric Space
11:50 | Conclusion Of Class

📚 Our Book Publications

🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹🔸🔹

👤 My Social Media Handles


✅Our YouTube Channels

📚 Important Course Playlists

📚 Following Topics Are Also Available

📷 My Equipment & Gear

Thanks For Watching My Video 🙏🏻
Like, Share & Subscribe 💯
Dr.Gajendra Purohit

[KhanMath]

Sir I am so happy.. Yesterday I search on YouTube about this topic but today here it is.. I am really very big fan of you sir... Thank You so much sir... You are the only guide in my preparation... Love you sir

[ashissamal]

Sir plz continue this topic it is vry important fr our university exam

[chiragaggarwal]

I am a student of bsc 4th sem. I am suffering from an eye disease called macular dystrophy.i am 60% visually handicapped and I will lose my vision in the coming years. I am not able to study properly. I try hard to srudy. My favourite subject is mathematics. Should I give IIT JAM exam. What competitive exam should I choose to give

[chandankumargupta]

Sir make a video on open and closed set, boundary points, conraction principle, construction of a real no as the completion of the incomplete metric space of retiooals in metric space

[umakant]

Quite experienced teacher... Lectures are awesome ♥️

[shailendrachaurasiya]

Sir Last example m x=y=1 v le sakte h???
So that x=y ho jayga

[KhanMath]

Sir which book will be good for Metric Space.. I am preparing for state PCS with mathematics as optional

[SandhyaKumari-svhm]

Sir, give us link of next videos of matric space...

[mathpi-rates]

Sir please give the link of related playlist of videos in the discription

[jeevanmaan]

Sir in last example humne x=1 or y=-1 liya hai agr hum y=1 lete hai to condition hold hoti aa

[unknonman]

Sir plz is playlist m yeh topics cover krdo ..
Exam aane wale h😭😭🙏🙏.
N Thank you ..👍
.
Definition and example of a metric space, Diameter of a set, Bounded set, Open sphere, Interior point
and Interior of a set, Derived and Closure of set, Closed set, Closed Sphere, Properties of Open and
Closed sets, Boundary point of set, Convergent and Cauchy sequences, complete metric space,
Cantor’s Intersection theorem. Dense subset, Baire Category theorem.
.
.
Limit of a function, Continuous function, theorem on necessary and sufficient conditions for continuity
of a function, Uniform continuity, Contracting mapping, Banach Fixed Point theorem, Equivalent
matrices, Compactness, Sequentially compactness, Totally Bounded space, Finite Intersection
properties.

[smritasingh]

Kyuki ye topics b sc m bhi h aur m sc m bhi h smjh m nhi aa rha h kya aur kaise kre aur sir telegram p apka channel mila h pr usme tayari ka math h plz help me sir

[rubeenaparveen]

You're an amazing teacher 😊 thank you so much

[cherrycheese]

Sir continuation of metric space... Connectedness, completeness and compactness🙏.. With specified theorem.. Plz sir🙏

[mahrukhkhan]

Sir last waly question may ager hum y ki value b 1 ly tou satisfied kerti ha condition

[Nishantmaurya]

Sir age bhi metric space ka video bna dijiye

[babechris]

I was waiting for it from months . Thanku sir

[dishatarafdar]

Sir plz upload videos on complete metric space, compactness, cauchy convergence criteria related to metric space...

[UttamKumar-jzoj]

Sir please continue this topics UNIT - I
Metric spaces: definition and examples. Sequences in metric spaces, Cauchy sequences. Complete
Metric Spaces. Open and closed balls, neighbourhood, open set, interior of a set. Limit point of a
set, closed set, diameter of a set, Cantor’s intersection theorem. Subspaces.
(2 questions)
UNIT - II
Continuous mappings, sequential criterion and other characterizations of continuity. Uniform
continuity. Homeomorphism, Contraction mappings, Banach Fixed point Theorem.
(1 questions)
UNIT - III
Geometry of complex numbers, regions in the complex plane, Limits and continuity of functions
of complex variable, Derivatives, Necessary and sufficient conditions for differentiability.
(1 questions)
UNIT - IV
Analytic functions, examples of analytic functions, Cauchy-Riemann equations, exponential
function, Logarithmic function, trigonometric function, derivatives of functions, bilinear
transformation, cross ratio, conformal mapping. (3 questions)

[komalkumari-wheo]

Thanks so much sir 🙏🏻 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻.... please continue the leacture 🙏🙏🙏🙏🙏. You are my all time favourite sir 🙏🏻🙏🏻🙏🏻🙏🏻....