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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
Link to download:
General Topology Notes
Notes Credit to SHAWN NEIL
Note: This pdf was recieved by me by SHAWN NEIL and was permitted to use .In any case of discrepancy first do inform and contact before flagging.
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