nullhomotopic map and factorization up to homotopy

1. Proposition

Let 20240110-nullhomotopic_map_and_factorization_up_to_homotopy_ad3eed98039b9cfe59b08856dd9226c73b0084b7.svg be topological spaces and 20240110-nullhomotopic_map_and_factorization_up_to_homotopy_e08d810fed313dafa6119deb03285ae027678f08.svg a continuous map. TFAE:

  1. 20240110-nullhomotopic_map_and_factorization_up_to_homotopy_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg is nullhomotopic
  2. 20240110-nullhomotopic_map_and_factorization_up_to_homotopy_ad6a03aaa8d3a8bd22f0e7659be6109d78aaf52a.svg can be factorized up to homotopy through 20240110-nullhomotopic_map_and_factorization_up_to_homotopy_e76a3a95873ecba75d94e0120c035c7ae7351774.svg
20240110-nullhomotopic_map_and_factorization_up_to_homotopy_5011ac27e4352a581471ea3164ee9d858d2ccbfc.svg

2. Proof

definitions

Date: nil

Author: Anton Zakrewski

Created: 2024-10-19 Sa 21:42