On Borsuk's non-retract theorem final version
arXiv:2407.13395
summary
The paper revisits Borsuk's non-retract theorem and demonstrates that, while a unit sphere cannot be a continuous retract of the unit closed ball, it can be a piecewise continuous retract.
Abstract
The classical Borsuk's non-retract theorem asserts that a unit sphere in is not a continuous retract of the unit closed ball. We will show that such a unit sphere is a piecewise continuous retract of the unit closed ball.
4 pages. arXiv admin note: substantial text overlap with arXiv:2312.03765
Topics & keywords
#topology#geometric topology#retraction theory#piecewise continuous maps#Borsuk's theoremBorsuk's non-retract theoremunit sphereunit closed ballpiecewise continuous retractcontinuous retract