#### Glasnik Matematicki, Vol. 52, No. 1 (2017), 179-183.

### GENERALIZED SUSPENSION THEOREM IN EXTENSION THEORY

### Leonard R. Rubin

Department of Mathematics,
University of Oklahoma,
Norman, Oklahoma 73019,
USA

*e-mail:* `lrubin@ou.edu`

**Abstract.**
A. Dranishnikov proved that for each
*CW*-complex *K* and metrizable compactum *X* with *Xτ K*,
it is true that *(X × I)τ(Σ K)*. Here, *Σ K*
means the suspension of *K* in the *CW*-category, and by
*X τ K* we mean that *K* is an absolute extensor for *X*.
We are going to
generalize this result so that *X* could be either a
stratifiable space or a compact Hausdorff space. Since all
metrizable spaces are stratifiable, then our result generalizes
Dranishnikov's.

**2010 Mathematics Subject Classification.**
54C55, 54C20.

**Key words and phrases.** Absolute co-extensor, absolute extensor,
absolute neighborhood extensor, CW-complex,
extension theory, paracompact, shrinking a cover, stratifiable space,
stratification, suspension.

**Full text (PDF)** (access from subscribing institutions only)
DOI: 10.3336/gm.52.1.13

**References:**

- C. J. R. Borges,
*On stratifiable spaces*,
Pacific J. Math. **17** (1966), 1-16.

MathSciNet
CrossRef

- J. G. Ceder,
*Some generalizations of metric
spaces*, Pacific J. Math. **11** (1961), 105-125.

MathSciNet
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- A. N. Dranishnikov,
*Extension of maps into CW-complexes*, Math. USSR-Sb. **74** (1993), 47-56.; Mat.
Sb. **182** (1991), 1300-1310 (Russian).

MathSciNet
CrossRef

- G. Gruenhage,
*Generalized metric spaces*, in
Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, 423-501.

MathSciNet
CrossRef

- S. T. Hu, Theory of retracts, Wayne State
University Press, Detroit, 1965.

MathSciNet

- I. Ivanšić and L. Rubin, Dimension, extension,
and shape, in preparation.

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