Lecture-9 || Metric space complete course || Closed set

Lecture-9 || Metric space complete course || Closed set Hello everyone , 📚 Welcome to Sharpen Maths — your trusted channel for Higher Mathematics, CSIR NET, GATE, IIT JAM, CUET, NBHM, MSc, BSc, State Assistant professor & PhD preparation. In this video, we discuss: 👉 Topic: Closed set 👉 Subject: Metric space 👉 Useful for: CSIR NET, GATE, IIT JAM, NBHM, MSc Mathematics, Research Entrance 🔹 This lecture will help you understand: ✔ Concepts clearly ✔ Problem-solving techniques ✔ Previous year question approach ✔ Exam-oriented preparation 📌 Subscribe to Sharpen Maths for: ✅ Complete courses in Higher Mathematics ✅ CSIR NET & GATE IIT JAM, NBHM PYQ solutions ✅ Strategy videos & toppers’ interviews ✅ Research & PhD guidance Important videos and playlist:- Preparation Strategy/ Interview CSIR_NET/GATE : https://www.youtube.com/watch?v=KUqqAG7lv6k&list=PLIPvdItY87lumJT0jcbdu-ybgi6MdBtgh what is connected and Pathconnectedness complete video : https://youtu.be/paVmAuKE-IQ Topologist sine curve : https://youtu.be/IS-i-9R2rGI Complex analysis complete course : https://youtube.com/playlist?list=PLIPvdItY87lsXpMpLC6CPHhKI2w9Khjnn Real analysis complete course :https://www.youtube.com/playlist?list=PLIPvdItY87lsSnWUFRBn_NdckTP-X9iXz Topology complete course :https://youtube.com/playlist?list=PLIPvdItY87ltPMiOrpc-hPtXoAc_uDe4d Measure Theory: https://www.youtube.com/watch?v=pMyiaexeLmE&list=PLIPvdItY87lu92DkiS5uOOXI9LJm73paw Functional Analysis: https://www.youtube.com/watch?v=AxDf31E6ShM&list=PLIPvdItY87lvXjxVmhsnDIzUgLo6IqZqX Field theory: https://www.youtube.com/watch?v=lc88M9lTKVQ&t=82s Number theory: https://www.youtube.com/watch?v=qhcgkHn9rLc&list=PLIPvdItY87lsgyfoZ9CENp-5zs2M5MzOV NBHM Linear algebra : https://www.youtube.com/watch?v=B9iPawYrQJw&list=PLIPvdItY87lsji7LyfbXbPo9xM3kciRzD TIFR Linear algebra: https://www.youtube.com/watch?v=48ZbXPa6HoE&list=PLIPvdItY87luPGMDkNudZgAN-uUER_c3k GATE 2022 solution: https://www.youtube.com/watch?v=Ps0mpYehwuI&list=PLIPvdItY87lvB5iA_Ubmaq0GtGMlFKgY5 CSIR-NET 2022 solution: https://www.youtube.com/watch?v=kfAPSnij3F4&list=PLIPvdItY87luIsuFCHWDHmIiUtqmE326F CSIR-NET 2020 solution: https://www.youtube.com/watch?v=Zcl8pd2fFAU&list=PLIPvdItY87ls_eGtxT0GwhqodbkcYn3eL IIT-JAM PYQS: https://www.youtube.com/watch?v=rJd4rfvQ8GQ&list=PLIPvdItY87luxZR5QHSk3SZi1EJDJJi4E GATE Linear algebra: https://www.youtube.com/watch?v=mJyTLQRQVXw&list=PLIPvdItY87lseGNXzyaEV0fRuF2QuUkGU CSIR-NET Linear algebra: https://www.youtube.com/watch?v=seVuSiEW8rg&list=PLIPvdItY87ltsFWeXjgKFq7uwyNWpJllq 🔔 Turn on notifications to never miss an update! 🔗 Follow Sharpen Maths for notes, pdf and important updates: 👉 YouTube:https://www.youtube.com/c/SharpenMaths1 👉 Telegram: https://t.me/Sharpenmaths1 👉 WhatsApp: https://whatsapp.com/channel/0029VaAXRkd7YScyPfjQRD1K 👉 Instagram: https://tinyurl.com/sharpenmaths 👉 Facebook: https://www.facebook.com/SharpenMaths #CSIRNET #GATEMathematics #IITJAM #MScMathematics #HigherMathematics #SharpenMaths #MathsLectures #MathsPreparation #NetJrf #GATE2026 #Metricspace #Closedset