### Categories

- Book & Article Reviews (3)
- Education (8)
- Mathematics (72)
- Algebra (6)
- Calculus (10)
- Combinatorics (26)
- Foundations (4)
- Games (7)
- Geometry (11)
- Logic (9)
- Probability (6)
- Ramsey Theory (3)
- Set Theory (8)
- Topology (11)
- Wednesday Problem (40)

- Meta (15)
- Philosophy (15)
- Popular (7)
- Recreation (35)

### Search Walks on Mind

### Like this blog?

- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
- Progress October 4, 2011
- Class-metric August 24, 2011
- Intellectual Lazyness August 22, 2011
- Time Limit: One Minute! August 17, 2011
- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
- 0.999999……=1? (continuation) July 10, 2011
- Walks on Planets July 5, 2011
- 0.999999….. = 1? July 3, 2011
- Prisoners’ problem 6 June 29, 2011
- I am back! June 28, 2011
- A non-associative “group” March 21, 2011
- Why I haven’t blogged March 21, 2011
- Doodling with Fractals and Persistent Worms. January 2, 2011
- Five groups November 23, 2010
- Splitting A Rectangle November 17, 2010
- Sphere November 10, 2010

### Tags

### Archives

- March 2017 (1)
- October 2011 (4)
- August 2011 (4)
- July 2011 (3)
- June 2011 (2)
- March 2011 (2)
- January 2011 (1)
- November 2010 (5)
- October 2010 (6)
- July 2010 (4)
- June 2010 (4)
- May 2010 (2)
- April 2010 (5)
- March 2010 (11)
- February 2010 (7)
- January 2010 (10)
- December 2009 (11)
- November 2009 (7)

# Monthly Archives: October 2011

## (Ir)rational Behavior of Calculation

We had the following set of exercises with a group of secondary school students (in Ressun lukio). Assume that a and b are positive real numbers. Then assume one of the following: (i) a and b are both rational (ii) … Continue reading

Posted in Algebra, Calculus, Education, Mathematics, Wednesday Problem
1 Comment

## The Product of Topological Spaces Does Not Obey Cancellation

Exercise 1. Find metric topological spaces [tex]A,B,C[/tex] such that [tex]A[/tex] is not homeomorphic to [tex]B[/tex], but [tex]A\times C[/tex] is homeomorphic to [tex]B\times C[/tex]. Exercise 2. Find path connected metric topological spaces [tex]A,B,C[/tex] such that [tex]A[/tex] is not homeomorphic to [tex]B[/tex], … Continue reading

Posted in Mathematics, Topology, Wednesday Problem
Leave a comment

## Wild Embeddings

Yesterday in a discussion in Komero we concluded that if f is an injective (one-to-one) map from the unit interval [0,1] to the Euclidean plane (or [tex]\mathbb{R}^n[/tex]), then the interval is homeomorphic with its image. The proof is as follows: … Continue reading

Posted in Algebraic Topology, Mathematics, Topology
Leave a comment