Remark on mappings not raising dimension of curves

Krasinkiewicz, J.

doi:10.2140/pjm.1974.55.479

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…On the other hand, if the image is a locally connected continuum, the pseudo-confluency is equivalent to condition (ii) of 3.3. Thus the theorem which follows also generalizes a theorem of [7].…”

Section: Theorem the Pseudo-confluent Image Of A Finitely Suslinian supporting

confidence: 57%

“…Let /: X -> F be a mapping of a space X onto a space F. The mapping / is said to be an inverse-arc function (see [6, p. Since all the dendrites are continua of Class A, our Corollary 4.9 strengthens the result of [7] and generalizes an earlier one [6,Theorem 8,p. 254].…”

Section: Theorem the Pseudo-confluent Image Of A Finitely Suslinian mentioning

confidence: 84%

“…Notice that the pseudo-confluent mappings may raise the dimension of one-dimensional continua that are not acyclic since, for instance, the 2-cell is the monotone image of a locally connected one-dimensional continuum. By 4.8, a result of [7] concerning the dendrites is generalized in Theorem 5.5. On the other hand, 5.5 generalizes a solution, reported in [12] and due to H. Cook, of a problem posed there (see [12, Problem 1, p. 102; 7]).…”

Section: Theorem the Pseudo-confluentmentioning

confidence: 99%

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Pseudo-Confluent Mappings and a Classification of Continua

Lelek

Tymchatyn

1975

Can. j. math.

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Section: Theorem the Pseudo-confluent Image Of A Finitely Suslinian supporting

confidence: 57%

Section: Theorem the Pseudo-confluent Image Of A Finitely Suslinian mentioning

confidence: 84%

Section: Theorem the Pseudo-confluentmentioning

confidence: 99%

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Pseudo-Confluent Mappings and a Classification of Continua

Lelek

Tymchatyn

1975

Can. j. math.

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“…. , k) with end-points p and p i} respectively, such that In the meantime, the original result with exactly the same proof was obtained independently by Krasinkiewicz [7,Theorem 2,p. 481].…”

Section: A Continuum X Is a Regular Curve If And Only If X Has Propermentioning

confidence: 62%

Weakly Confluent Mappings and Atriodic Suslinian Curves

Cook¹,

Lelek²

1978

Can. j. math.

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There are theorems in which some classes of topological spaces are characterized by means of properties of mappings of these spaces into a single space. For example, it is well known that a compactum X is at most n-dimensional if and only if no mapping of X irto an (n + l)-cube has a stable value [5, Theorems VI. 1-2, pp. 75-77]. Also, a curve X is tree-like if and only if no mapping of X into a figure eight is homotopically essential [1, Theorem 1, pp. 74-75; 8, p. 91]. By a curve we mean any at most 1-dimensional continuum; a continuum is a connected compactum; a compactum is a compact metric space, and a mapping is a continuous function. The aim of the present paper is to prove another theorem of this type. We distinguish a class of curves and show that it is characterized by imposing the condition that no weakly confluent mapping [13] can transform the given curve onto a simple triod (see 2.4). A related result is applied to a generalized branch-point covering theorem (see 3.2). In addition, two results are obtained in which we establish some characterizations of weakly confluent images and preimages of the product of the Cantor set and an arc (see 1.1 and 2.2). Continua that are such images turn out to be identical with regular curves (see 1.3).

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Dimension theory

Pasynkov¹,

Fedorchuk²,

Филиппов³

1982

J Math Sci

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The T-equivalence and J-iterations introduced for a bifunctor Tenable one to deduce a "shifting property" from which one gets the "long exact sequence of homology." Also, the appropriate lemma of Schanuel is proved, from which one can develop a T-dimension theory. These notions are useful in proving known duality homomorphisms and may serve to get some new ones. For one purpose, they unify the methods of studying the various common dimensions.

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Remark on mappings not raising dimension of curves

Cited by 3 publications

References 6 publications

Pseudo-Confluent Mappings and a Classification of Continua

Pseudo-Confluent Mappings and a Classification of Continua

Weakly Confluent Mappings and Atriodic Suslinian Curves

Dimension theory

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