Continua and their non-separating subcontinua

  • 50 Pages
  • 4.80 MB
  • English
Państwowe Wydawn. Naukowe , Warszawa
Continuity, Metric s
StatementD. E. Bennett and J. B. Fugate.
SeriesDissertationes mathematicae = Rozprawy matematyczne -- 149, Rozprawy matematyczne -- 149.
ContributionsFugate, J. B.
The Physical Object
Pagination50 p. :
ID Numbers
Open LibraryOL13627327M

Additional Physical Format: Online version: Bennett, D.E. Continua and their non-separating Continua and their non-separating subcontinua book. Warszawa: Państwowe Wydawn. Naukowe,   The notion of a terminal continuum, as defined by D.E. Bennett and J.B. Fugate, is used to introduce extremal continua, a class of non-separating subc Cited by: 4.

[1] D. Bennett, A sufficient condition for countable-set aposyndesis, Proc. Amer. Math. Soc. 32 (), pp. [2] R. Bing, Snake-like continua, Duke Math.

continua of M such that Mn+1 Mn contains a non-separating open subset of M for each n 2 N. (7) Either M is an 1-od or there is an infinite increasing sequence M1;M2;M3; of non-separating subcontinua of M such that Mn+1 Mn contains a non-separating open subset of M for each n 2 N.

(8) ć M is the union of an infinite monotonic collection. Continua and their non-separating subcontinua. Article. D.E. Bennett A mapping between continua is said to be feebly monotone if whenever the range is the union of two proper subcontinua.

The family of Wilder continua in the cube I n and its two subfamilies—of continuum-wise Wilder continua and of hereditarily arcwise connected continua—are recognized as coanalytic absorbers in the hyperspace C (I n) of subcontinua of I n for 3 ≤ n ≤ ∞.In particular, each of them is homeomorphic to the set of all nonempty countable closed subsets of the unit interval I.

The hyperspaces of hereditarily decomposable continua and of decomposable subcontinua without pseudoarcs in the cube of dimension greater than 2 are homeomorphic to the Hurewicz set of all.

cutpoints of inv ariant subcontinua of polynomial julia sets9 Theorem is well-known (see, e.g., Corollary of [Nad92]).

Theorem (Boundary Bumping Theorem). This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the th Annual Joint Mathematics Meetings held in Cincinnati, Ohio.

It also features the Houston Problem Book which includes a recently updated set of problems accumulated over several years at the University of Houston.;These proceedings and.

Continua and their non-separating subcontinua. Interrelations between three concepts of terminal continua and their behaviour, when the underlying continuum is confluently mapped, are studied.

with exactly two non-separating points) and aposyndetic continua have the Wilder property and plane examples were given of Wilder continua thatare neither arcwise connected noraposyndetic [16], [18]. Moreover, by [16, Corollary 2], one can observe that a nondegenerate continuum is Date: Continua and their non-separating subcontinua book Mathematics Subject Classification.

continuum that is separated by none of its subcontinua. If A is a subset of M then T(A) consists of A together with all points x G M such that there does not exist an open set U and a continuum H such that x G UCHCM — let T°(x) = x, and T"(x) = T(Tn~l(x)) where «is a positive integer.

If A is a. The notion of a terminal continuum, as defined by D.E. Bennett and J.B. Fugate, is used to introduce extremal continua, a class of non-separating subcontinua of a continuum. Continua homeomorphic to every of their nondegenerate subcontinua are named hereditarily equivalent.

As early as S. Mazurkiewicz posed a question as to whether every hereditarily equivalent continuum is an arc [Problème 14, Fund. Math. 2 (), ]. Conditions are studied concerning mappings between continua under which the image of an extremal continuum in the domain is an extremal continuum in t.

Topology and its Applications 47 () 69 North-Holland Terminal continua and quasi-monotone mappings J.J. Charatonik Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, Wroclaw, Poland Received 20 March Revised 16 August Abstract Charatonik, J.J., Terminal continua and quasi-monotone mappings, Topology and its Applications 47 () morphic, homogeneous, non-separating continua with decompo­ sition space a simple closed curve.

This led Bing and Jones [5] to show that there does exist a circle of pseudo-arcs, i.e.

Description Continua and their non-separating subcontinua EPUB

a homogeneous, circle­ like, continuum with a continuous decomposition into pseudo­ arcs such that the decomposition space is a simple closed curve.

called the Whitney continua of X. In Section 2 we characterize the separating points of ~-l(t) in terms of their separating properties as subcontinua of X.

The rest of the paper contains applications of this result.

Details Continua and their non-separating subcontinua EPUB

In Section 3 we obtain some information about the Whitney continua of arc-like and circle-like continua. Section. Book (UHPB), a good reference for further problems.

If X has only chainable proper subcontinua and (?), geneous, non-separating plane continuum, does there exist a continuous collection of continua, each homeomorphic to.

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M, filling up the plane. Does the plane contain a (homo­. This survey is devoted to divisions of the theory of continua associated with snake- like, tree- like, and circlelike bicompacta, homogeneous spaces, hyperspaces of continua, and Whitney maps.

Characterizations of semiatriodic and unicoherent continua are given, as well as necessary and sufficient conditions for a subcontinuum of a semiatriodic and unicoherent continuum M to lie within the interior of a proper subcontinuum of M.

Continua and their non-separating subcontinua, Dissertationes Math. [2]R. Bing, Snake. This book is a significant companion text to the existing literature on continuum theory.

It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua. The chosen approach is based on convex planar continua and their subcontinua as primitive notions.

In a first step convex planar continua are mathematized and represented by ordered sets. In a second step ‘points’ are deduced as limits of continua by methods of Formal Concept Analysis. subcontinua, and has the fixed point property. Like a simple closed curve it is homogeneous and has arbitrarily small open covers of circular chains.

It is ubiquitous. (Bing showed [22] that in the category sense almost all continua are pseudo-arcs. Wayne Lewis recently proved that. Continua definition: a continuous series or whole, no part of which is perceptibly different from the | Meaning, pronunciation, translations and examples.

spect to their subcontinua with interiors and the way these subcon-tinua separate points and sets. The structure of all solenoids with respect to these properties is the same. All solenoids are indecom-posable and have only arcs for proper subcontinua.

The product of two non-degenerate continua is aposyndetic, and the product of. Cook, in the University of Houston problem book, asks (Problem 5) "Can continua, when embedded in the plane, necessarily leave many points inacces-sible from the complement [6].

Hereditarily decomposable chainable continua their layers and so on, as in [10 and 8]. Define 3o to be {X}. If a = ß + 1 then J2fa will consist of the. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

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Assume that a nondegenerate continuum X is homeomorphic to each of its nondegenerate subcontinua. Must then X be either an arc or a pseudo-arc?. Continua homeomorphic to every of their nondegenerate subcontinua are named hereditarily early as S.

Mazurkiewicz posed a question as to whether every hereditarily equivalent continuum is an arc [Problème 14, Fund. Math. tree-like continua do not admit expansive homeomorphisms. Similarly, homeomorphisms that stretch subcontinua of 2-separating plane continua must have some folding.

This is the idea in the proof of the main result. Characterization of 1-dimensional 2-separating plane continua We begin with several important definitions. Whyburn’s book [18]). Also concepts of weakly monotone and of confluent mappings between continua are known for years and were studied by a number of authors.

The reader is referred to Ma´ckowiak dissertation [12] for interrelations between these classes of mappings and their basic properties. Some properties related to almost monotone and.Five continua are used to distinguish nothing from something, and.

more specifically to distinguish between non-places—places, things—non-things, people—non-people, and services—non. services. The left hand pole of each the following is the something.

end of the continuum and the right is .of all subcontinua of X, i.e., of all connected elements of 2X, and, for a point p2X,we denote by C.p;X/the family of all subcontinua ofXcontaining the point p.

The reader is referred to Nadler’s book [9] for needed information on the structure and properties of hyperspaces. A mapping f:X!Ybetween continua Xand Yis said to be.