CSIR-NET Dec 2025 Part C | Topology Important Question | QID 916710210 | Finite Complement Topology

Описание: In this video, we solve a CSIR-NET December 2025 Mathematics Part C question based on Topology, focusing on the finite complement topology and important separation axioms.

R with usual topology is normal.
R with Finite Complement Topology is T1.
R with Finite Complement Topology is not Hausdorff or T2
R with Finite Complement Topology is not T3
R with Finite Complement Topology is not T4
R with Finite Complement Topology is connected
R with Finite Complement Topology is not Regular
R with Finite Complement Topology is not normal
R with Finite Complement Topology is compact

Any set X with Finite Complement Topology is T1.
An infinite set X with Finite Complement Topology is not Hausdorff or T2
An infinite set X with Finite Complement Topology is not T3
An infinite set X with Finite Complement Topology is not T4
An infinite set X with Finite Complement Topology is connected
An infinite set X with Finite Complement Topology is not Regular
An infinite set X with Finite Complement Topology is not normal
Any set X with Finite Complement Topology is always compact


📌 Question ID: 916710210
📌 Topics covered:
• Euclidean topology
• Finite complement topology
• Normal, Regular and Hausdorff spaces
• Continuity of identity map
• Core topology concepts for CSIR-NET Part C
This problem helps you clearly understand how different topologies behave on ℝ and how properties like regularity, normality and Hausdorffness are tested in competitive exams.

👉 Very useful for CSIR-NET, GATE, JAM, MSc entrances, and PhD coursework.
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