P-embeddings, AR and ANR spaces

Stramaccia, Luciano

doi:10.4310/hha.2003.v5.n1.a9

Cited by 4 publications

(2 citation statements)

References 5 publications

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“…Theorem 2.3. (See [6]) Let A be a closed subspace of metrizable space E and O be an ANR space. Then A has a homotopy extension property in E with respect to a space O.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Saif,

Kilicman

2010

Preprint

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Let f : E −→ O be a Hurewicz fibration with a fiber space Fr o and a lifting function L f . The Lf −function ΘL f of f is defined by the restriction map of L f on the space Ω(O, ro) × Fr o × {1}. The purpose of this paper is to give some results which show the role of Lf −functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of polyhedron spaces.

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“…Theorem 2.3. (See [6]) Let A be a closed subspace of metrizable space E and O be an ANR space. Then A has a homotopy extension property in E with respect to a space O.…”

Section: Preliminariesmentioning

confidence: 99%

“…If O is an absolute neighborhood retract (ANR) space, then S(O) is an ANR. Similarly, for polyhedron property, for more details see [5,6]. Dold's theorem is one of the famous solutions for the classification problem in fiber bundles over the n−sphere bases S n , (see [10]).…”

Section: Introductionmentioning

confidence: 99%

On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Saif,

Kilicman

2010

Preprint

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Shape Theory

Gevorgyan

2021

J Math Sci

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Spaces of functions and sections with paracompact domain

Smrekar

2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We study spaces of continuous functions and sections with domain a paracompact Hausdorff k-space $X$ and range a nilpotent CW complex $Y$ , with emphasis on localization at a set of primes. For $\mathop {\rm map}\nolimits _\phi (X,\,Y)$ , the space of maps with prescribed restriction $\phi$ on a suitable subspace $A\subset X$ , we construct a natural spectral sequence of groups that converges to $\pi _*(\mathop {\rm map}\nolimits _\phi (X,\,Y))$ and allows for detection of localization on the level of $E^2$ . Our applications extend and unify the previously known results.

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P-embeddings, AR and ANR spaces

Cited by 4 publications

References 5 publications

On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Shape Theory

Spaces of functions and sections with paracompact domain

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