
Course Outline /Schedule (Weekly) Planned Learning Activities 
 Week  Subject  Student's Preliminary Work  Learning Activities and Teaching Methods 

1 
Review of some topological concepts. Subbase and the concept of neighborhood. 
Review of the relevant pages from sources 
Narration and discussion 

2 
First and Second countable spaces. Separable spaces. 
Review of the relevant pages from sources 
Narration and discussion 

3 
Product spaces and weak topologies. 
Review of the relevant pages from sources 
Narration and discussion 

4 
Embedding theorems. Convergence of sequences. Sequential continuity. 
Review of the relevant pages from sources 
Narration and discussion 

5 
Nets and Convergence. Filters and convergence. 
Review of the relevant pages from sources 
Narration and discussion 

6 
Problemsolving. T0 and T1spaces. 
Review of the relevant pages from sources 
Narration and discussion 

7 
T2 (Hausdorff), regular, T3spaces. 
Review of the relevant pages from sources 
Narration and discussion 

8 
Midterm exam 
topics discussed in the lecture notes and sources again 
Exam 

9 
Completely regular, normal spaces and Jhon´s Lemma. and T4spaces. 
Review of the relevant pages from sources 
Narration and discussion 

10 
Tychonoff spaces and T4 spaces 
Review of the relevant pages from sources 
Narration and discussion 

11 
The compactness andthe finite intersection property, and the relationship between the compactness and convergence. HeineBorel Theorem. 
Review of the relevant pages from sources 
Narration and discussion 

12 
HeineBorel Theorem. The relationship between compactness and Hausdorff spaces. 
Review of the relevant pages from sources 
Narration and discussion 

13 
Fundamental properties of compact spaces. 
Review of the relevant pages from sources 
Narration and discussion 

14 
local compactness 
Review of the relevant pages from sources 
Narration and discussion 

15 
Consequences of local compactness 
Review of the relevant pages from sources 
Narration and discussion 

16/17 
Final exam 
topics discussed in the lecture notes and sources again 
Exam 

