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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
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1 |
Review of some topological concepts. Sub-base and the concept of neighborhood. |
Review of the relevant pages from sources |
Narration and discussion |
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2 |
First and Second countable spaces. Separable spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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3 |
Product spaces and weak topologies. |
Review of the relevant pages from sources |
Narration and discussion |
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4 |
Embedding theorems. Convergence of sequences. Sequential continuity. |
Review of the relevant pages from sources |
Narration and discussion |
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5 |
Nets and Convergence. Filters and convergence. |
Review of the relevant pages from sources |
Narration and discussion |
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6 |
Problem-solving. T0 and T1-spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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7 |
T2 (Hausdorff), regular, T3-spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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8 |
Mid-term exam |
topics discussed in the lecture notes and sources again |
Exam |
|
9 |
Completely regular, normal spaces and Jhon´s Lemma. and T4-spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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10 |
Tychonoff spaces and T4 spaces |
Review of the relevant pages from sources |
Narration and discussion |
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11 |
The compactness andthe finite intersection property, and the relationship between the compactness and convergence. Heine-Borel Theorem. |
Review of the relevant pages from sources |
Narration and discussion |
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12 |
Heine-Borel Theorem. The relationship between compactness and Hausdorff spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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13 |
Fundamental properties of compact spaces. |
Review of the relevant pages from sources |
Narration and discussion |
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14 |
local compactness |
Review of the relevant pages from sources |
Narration and discussion |
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15 |
Consequences of local compactness |
Review of the relevant pages from sources |
Narration and discussion |
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16/17 |
Final exam |
topics discussed in the lecture notes and sources again |
Exam |
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