A construction of noncontractible simply connected cell-like two-dimensional Peano continua

• Autorzy: Katsuya Eda , Umed H. Karimov , Dušan Repovš
• Języki publikacji: EN

Abstrakty

EN

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.

Kategorie tematyczne

• 55M15: Absolute neighborhood retracts
• 54G15: Pathological spaces
• 57N60: Cellularity
• 54F15: Continua and generalizations
• 55Q52: Homotopy groups of special spaces
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 195
• Numer: 3
• Strony: 193-203

Daty

wydano

2007

Twórcy

autor

Katsuya Eda

• School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan

autor

Umed H. Karimov

• Institute of Mathematics, Academy of Sciences of Tajikistan, Ul. Ainy 299A, Dushanbe 734063, Tajikistan

autor

Dušan Repovš

• Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana 1001, Slovenia

Identyfikatory

DOI

10.4064/fm195-3-1