Structure of hereditarily infinite dimensional spaces

Yohe, J. M.

doi:10.1090/s0002-9939-1969-0236896-9

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…More precisely, the main results of this paper are the following theorems. Theorem 1.2 is an improvement of a result from [12], where we have constructed continuum many topologically different HI hereditarily SID Cantor manifolds, answering a question of Yohe [17]. Earlier, Chatyrko and the author constructed in [5] a family {X s : s ∈ S} of cardinality continuum of hereditarily SID Cantor manifolds such that no open subset of X s embeds in X s for s = s ; however, these continua were not HI.…”

Section: Introductionmentioning

confidence: 76%

Collections of higher-dimensional hereditarily indecomposable continua, with incomparable Fréchet types

Pol¹

2005

Topology and its Applications

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We construct a family {Y s : s ∈ S} of cardinality 2 ℵ 0 of hereditarily indecomposable continua which are: (a) n-dimensional Cantor manifolds, for any given natural number n, or (b) hereditarily strongly infinite-dimensional Cantor manifolds, or else (c) countable-dimensional continua of every given transfinite inductive dimension, small or large, such that if h : Y s → Y s is an embedding then s = s and h is the identity.

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Section: Introductionmentioning

confidence: 76%

Collections of higher-dimensional hereditarily indecomposable continua, with incomparable Fréchet types

Pol¹

2005

Topology and its Applications

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“…It might be remarked that Proposition 2 can also be obtained by modifying the constructions in § §3, 4, and 5 to use M-cells instead of HID continua; however, there is little point in doing that since the proof given here is neater and more intuitively appealing. 7. Questions.…”

Section: Corollarymentioning

confidence: 99%

“…In a previous paper [7], we studied the structure of HID spaces. In this paper, we consider the behavior of HID spaces under monotone mappings.…”

Section: Introductionmentioning

confidence: 99%