Locally Contractible Spaces That are Absolute Neighborhood Retracts

Haver, William E.

doi:10.2307/2038681

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Cited by 14 publications

(9 citation statements)

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“…[6], [8], and [18]. In the second section of the paper we show that HPiiM) is homeomorphic to HpLiM) x ¡2 which will complete the proof that HpliM) is an /(-manifold.…”

mentioning

confidence: 68%

The group of 𝑃𝐿-homeomorphisms of a compact 𝑃𝐿-manifold is an 1^{𝑓}₂-manifold

Keesling¹,

Wilson²

1974

Trans. Amer. Math. Soc.

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“…[6], [8], and [18]. In the second section of the paper we show that HPiiM) is homeomorphic to HpLiM) x ¡2 which will complete the proof that HpliM) is an /(-manifold.…”

mentioning

confidence: 68%

The group of 𝑃𝐿-homeomorphisms of a compact 𝑃𝐿-manifold is an 1^{𝑓}₂-manifold

Keesling¹,

Wilson²

1974

Trans. Amer. Math. Soc.

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“…As a convex subset of a linear space, C is contractible and locally contractible. Since every cr-fd-compact locally contractible metric space is an ANR [10], C is an AR. By 3.4, C contains a skeletoid for finite-dimensional compacta.…”

Section: 1mentioning

confidence: 99%

Some applications of the topological characterizations of the sigma-compact spaces 𝑙²_{𝑓} and Σ

Curtis¹,

Dobrowolski²,

Mogilski³

1984

Trans. Amer. Math. Soc.

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ABSTRACT. We use a technique involving skeletoids in cr-compact metric ARs to obtain some new examples of spaces homeomorphic to the cr-compact linear spaces I2, and E. For example, we show that (1) every No-dimensional metric linear space is homeomorphic to ¡?; (2) every cr-compact metric linear space which is an AR and which contains an infinite-dimensional compact convex subset is homeomorphic to E; and (3) every weak product of a sequence of cr-compact metric ARs which contain Hubert cubes is homeomorphic to E.

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“…Proposition 1 is a consequence of the observation that contractible groups are also locally contractible [7] and a result of Haver [11] that a-fd-compact locally contractible spaces are ANRs.…”

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confidence: 93%

Examples of topological groups homeomorphic to 𝑙^{𝑓}₂

Dobrowolski¹

1986

Proc. Amer. Math. Soc.

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Abstract.We prove that the following spaces are homeomorphic to 12'-(1) the group of piecewise continuous autotransformations of [-1,1] preserving Lebesgue measure, and (2) certain subgroups obtained as group spans of linearly independent arcs in linear spaces. These are consequences of our discussion of the problem whether o-fd-compact locally contractible metric groups must be either finite-dimensional or locally homeomorphic to l{.

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Locally Contractible Spaces That are Absolute Neighborhood Retracts

Abstract: Abstract.It is shown that every locally contractible metric space that is the countable union of finite dimensional compacta is an absolute neighborhood retract.

Cited by 14 publications

References 0 publications

The group of 𝑃𝐿-homeomorphisms of a compact 𝑃𝐿-manifold is an 1^{𝑓}₂-manifold

The group of 𝑃𝐿-homeomorphisms of a compact 𝑃𝐿-manifold is an 1^{𝑓}₂-manifold

Some applications of the topological characterizations of the sigma-compact spaces 𝑙²_{𝑓} and Σ

Examples of topological groups homeomorphic to 𝑙^{𝑓}₂

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