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3 Bulletin of the Polish Academy of Sciences. Mathematics

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Strong cohomological dimension

Dydak J., Koyama A.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 2

183-189

We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that Inde X = dim[sub G] X if X is a separable metric ANR and G is a countable Abelian group. Hence dim[sub Z] X = dim X for any separable metric ANR X.

Inverse sequences and absolute co-extensors

Ivanšic I., Rubin R.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 3

243-259

Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = lim X. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map ƒ : A → K from a closed subset A of X extends to a map F : X → K. Incase K is & polyhedron |/C|cw (the set \K\ with the weak topology CW), we determine a similar characterization that takes into account the simplicial structure of K.

Moore spaces and cohomological dimension

Miyata T.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

231-235

For each n [is a greater than or equal to] 1 and prime p, we construct a compact metric space X with the cohomological dimension modulo p, dim[sub Z/p] X [is less than or equal to] n, for which the Moore space M(Z/p,n) is not an extensor.