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# Topological Spaces starter

3.8
3.8/5
(6 reviews)
54 students

## 9.0

CourseMarks Score®

9.5

Freshness

7.3

Feedback

9.6

Content

Platform: Udemy
Video: 15h 50m
Language: English
Next start: On Demand

## CourseMarks Score®

9.0 / 10

CourseMarks Score® helps students to find the best classes. We aggregate 18 factors, including freshness, student feedback and content diversity.

## Freshness Score

9.5 / 10
This course was last updated on 11/2021.

Course content can become outdated quite quickly. After analysing 71,530 courses, we found that the highest rated courses are updated every year. If a course has not been updated for more than 2 years, you should carefully evaluate the course before enrolling.

## Student Feedback

7.3 / 10
We analyzed factors such as the rating (3.8/5) and the ratio between the number of reviews and the number of students, which is a great signal of student commitment.

New courses are hard to evaluate because there are no or just a few student ratings, but Student Feedback Score helps you find great courses even with fewer reviews.

## Content Score

9.6 / 10
Video Score: 10.0 / 10
The course includes 15h 50m video content. Courses with more videos usually have a higher average rating. We have found that the sweet spot is 16 hours of video, which is long enough to teach a topic comprehensively, but not overwhelming. Courses over 16 hours of video gets the maximum score.
Detail Score: 9.3 / 10

The top online course contains a detailed description of the course, what you will learn and also a detailed description about the instructor.

Extra Content Score: 9.5 / 10

Tests, exercises, articles and other resources help students to better understand and deepen their understanding of the topic.

This course contains:

3 articles.
0 resource.
0 exercise.
0 test.

## Description

If we have a set of points \$X\$, how can we make a precise notion of closeness and locality? We can define a notion of distance between individual points and have those notions follow as consequences. However, we can be more subtle and define whats known as a emph{topology} on this set making \$X\$ emph{topological space}, which makes precise those notions of closeness, locality, and therefore the notion of continuity (the preserving of closeness) in \$X\$ directly. Subsequent notions which can also be represented in this setting are that of connectedness (and therefore disconnectedness), compactness and limits.

Look at the beginnings of topology and topological spaces. We cover much of Munkres Chapter 2 and its exercises but with reflection and introspection. The ideas are known by all mathematicians and yet the presentation is considered too new for most university students but at the same time looking back on it now is quite strikingly out of date. The basics are still the same but they appear different, the focus is on the concrete spaces and less on the functions between them. Some perspective is added with category theory in mind but much of it is looking closely at the foundations with a classical perspective.

Lots of the earlier basic examples of topological spaces are examined in detail.
Product spaces, quotient spaces, subspaces are all defined and examined topologically.
Continuous functions, closed sets, open sets, Hausdorf space, T1 space, limit point, basis, base, sub base,
Metric spaces and metric topology is currently omitted.
Connectedness and compactness is omitted.

This is for beginners in topology but not necessarily beginners in mathematics especially if you have not used you mind much before.

#### You will learn

✓ Define a topological space, topology, open set, closed set, continuous function
✓ Understand and use the notion of a base or basis of neighbourhoods
✓ Various universal constructions including product, quotient and subspace topology
✓ Definition chase, basic proofs, solve simple exercises with unfamiliar terms

#### Requirements

• Growth mindset
• Abstract thinking and thoughtfulness
• Decent short term and long term memory
• Experience in abstract algebra and other high level maths will be helpful but not essential
• Experience in analysis helpful but not essential
• Experience in calculus helpful but not essential
• Experience in Linear algebra helpful but not essential

#### This course is for

• Students who are trying to grasp abstractions in maths at a high level
• Students who want to fill in gaps from their knowledge
• Students who want to be mathematicians
• Smart students

#### How much does the Topological Spaces starter course cost? Is it worth it?

The course costs \$14.99. And currently there is a 82% discount on the original price of the course, which was \$84.99. So you save \$70 if you enroll the course now.

#### Does the Topological Spaces starter course have a money back guarantee or refund policy?

YES, Topological Spaces starter has a 30-day money back guarantee. The 30-day refund policy is designed to allow students to study without risk.

#### Are there any SCHOLARSHIPS for this course?

Currently we could not find a scholarship for the Topological Spaces starter course, but there is a \$70 discount from the original price (\$84.99). So the current price is just \$14.99.

#### Who is the instructor? Is Dr Michael Sun a SCAM or a TRUSTED instructor?

Dr Michael Sun has created 29 courses that got 49 reviews which are generally positive. Dr Michael Sun has taught 2,488 students and received a 3.7 average review out of 49 reviews. Depending on the information available, Dr Michael Sun is a TRUSTED instructor.

#### Dr Michael Sun

Mathematician
Join me for meaningful learning that will have lasting value.
Much of the content takes a student through the experience of solving a problem from scratch, learning a concept rigorously or applying a concept to a problem. This process is filmed and presented here with basically no editing. To be truly great at maths you cannot just memorise disconnected facts you need to learn how to think, how to link and how to learn. For younger students we have the luxury of applying the things we learn in math olympiad problems. I look forward to seeing you in class!
Background
PhD, first in graduating class USA (UOregon)
This is also where I learned to play Basketball.
M.Sc by research, fastest possible with publication, USyd, AUS
B.Sc (Honours), University Medal, all High Distinctions, USyd AUS
ATAR 99.95 NSW Australia
Postdoctoral research fellow Germany (Unimuenster)
Visiting scholar China (ECNU Shanghai)
Research publications and conference attendance.

## 9.0

CourseMarks Score®

9.5

Freshness

7.3

Feedback

9.6

Content

Platform: Udemy
Video: 15h 50m
Language: English
Next start: On Demand

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