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Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda, Kazuhiro Kawamura (2000)

Fundamenta Mathematicae

For the n-dimensional Hawaiian earring ℍ n , n ≥ 2, π n ( ℍ n , o ) ≃ ℤ ω and π i ( ℍ n , o ) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then H n ( X ∨ Y ) ≃ H n ( X ) ⊕ H n ( Y ) ⊕ H n ( C X ∨ C Y ) for n ≥ 1.

On the first homology of Peano continua

Gregory R. Conner, Samuel M. Corson (2016)

Fundamenta Mathematicae

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the...

On universality of countable and weak products of sigma hereditarily disconnected spaces

Taras Banakh, Robert Cauty (2001)

Fundamenta Mathematicae

Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power X ω of any subspace X ⊂ Y is not universal for the class ₂ of absolute G δ σ -sets; moreover, if Y is an absolute F σ δ -set, then X ω contains no closed topological copy of the Nagata space = W(I,ℙ); if Y is an absolute G δ -set, then X ω contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable power X ω of...

Parity complexes

Ross Street (1991)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Currently displaying 21 – 40 of 52