General Topology Notes

General Topology Notes Mathematics 

Here we are presenting you general Topology Notes in pdf form.
Its comparatively hard to find general topology notes because of low online demand or usages.
General Topology is widely used in various mathematics field and for educational purpose. Used for b.sc and m.sc in mathematics.
Also used in Csir - Net and ugc net other competition exams.
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Contents of file/ lecture Notes
1 Lecture 
1.1 History of Topology
1.2 Set Theoretic Preliminaries 
1.3 Relations and Functions 
1.4 Cardinality and Operations on Sets 
2 Lecture
2.1 Logic and Techniques of Proof 
2.2 Topology on a Set
2.3 Open and Closed Sets 
3 Lecture
3.1 Set Theoretic Preliminary
3.2 Interior and Closure 
3.3 Exterior and Boundary 
3.4 Examples 
4 Lecture
4.1 Interior, Closure, Exterior, and Boundary Points 
4.2 Cluster Points and Isolated Points 
5 Lecture
5.1 The Isolated Points of a Space 
5.2 Introduction to Connectedness 
5.3 Introduction to Separation Condition
6 Lecture 
6.1 Dense Subsets 
6.2 Nowhere Dense Subsets .
6.3 Separable Spaces 
6.4 Equivalent Statements About Open and Closed Sets 
6.5 More on Cluster Points and Isolated Points 

7 Lecture 
7.1 Basis for a Topology 
7.2 The Digital Line Topology 
8 Lecture
8.1 More Properties of a Basis 
8.2 Calculating the Interior and Closure of Unions and Intersections 
8.3 Properties of the Digital Line 
9 Lecture
9.1 More Properties of the Digital Line 
9.2 Relations on a Set 
9.3 Introduction to the Order Topology 
10 Lecture
10.1 More Properties of Posets and Simply Ordered Sets 
10.2 Properties of the Order Topology 
11 Lecture
11.1 Compositions, Inverses, and Restrictions of Functions .
11.2 Finite Sets 
12 Lecture
12.1 The Cofinite Topology 
12.2 Countable Sets 
12.3 Introduction to the Cocountable Topology 
13 Lecture 
13.1 Properties of the Cofinite and Cocountable Topologies 
13.2 More Countability Conditions 
13.3 The Order Topology on Q 
14 Lecture
14.1 More on Local Bases 
14.2 The Order Topology on Q and R
14.3 Introduction to the Subspace Topology 
15 Lecture
15.1 Properties of the Subspace Topology
15.2 Convex Subsets and Subbases 
16 Lecture
16.1 Inherited Properties of Subspaces
16.2 Functions Acting on Sets 
16.3 Introduction to Continuity 
17 Lecture
17.1 More on Continuity 
17.2 The Initial Topology
17.3 Introduction to the Product Topology on Finite Products 
18 Lecture 
18.1 Continuous Functions 
18.2 Properties of the Product Topology on a Finite Product Set 
19 Lecture
19.1 More Properties of the Product Topology on a Finite Product Set 
19.2 Generalized Cartesian Products 
19.3 The Product and Box Topologies 
20 Lecture
20.1 Properties of the Box and Product Topologies 
20.2 Introduction to Equivalence Relations 
21 Lecture 
21.1 Homeomorphisms and Topological Invariants 
21.2 Examples 
22 Lecture
22.1 More on Homeomorphisms and Topological Invariants 
22.2 The Sorgenfrey Line Rl
22.3 The Michael Line RM 
23 Lecture 
23.1 Additional Characteristics of Regularity and Normality 
23.2 Porperties of the Real Line R 
23.3 Properties of the Sorgenfrey Line Rl
23.4 Properties of the Michael Line RM
23.5 The K-topology on R 
24 Lecture
24.1 Additional Properties of the Sorgenfrey Line Rl
24.2 Additional Properties of the Michael Line RM 
24.3 The K-topology on R 
24.4 A Few Counterexamples 
24.5 The Final (Inductive) Topology 



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General Topology Notes
Notes Credit to SHAWN NEIL

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