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Topology Exercise: The Apartment.


Topology Exercise: The Four-Floor House

By Justin Merchan

Abstract

The objective of this example is to exercise our ability to analyze, visualize and solve problems that involve certain area by applying concepts of topology and the manipulation of areas. This exercise is developed around the idea of a homotopy equivalence.

Introduction

We are given a four-floor house, that we will be calling $X$. Each floor has a stair that connects the superior floor with the one below itself, excluding the first and the terrace.

Exercise:
Given space $X$, what simple space $Y$ $\simeq$ $X$. 

Sketch of the four-floor house
*This exercise is inspired on the exercise described by John Redford in his YouTube video "A Homotopy Problem" (Link Below) that I also recommend to check if you liked this problem.

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1 comment:

  1. HCSeptember 11, 2017 at 4:48 PM

    This is a very interesting problem. Can you explain a little better the layout of this house? I am not sure if I understand where the terrace is. Also, there seem to be two stairs in some floors? Clarify a little bit the drawing.

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