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Absorber Characterization of Subcontinua with Connected Boundaries

For a pi-n-Euclidean unicoherent Peano continuum with n at least 2, the proper subcontinua with connected boundary form exactly the pseudo-interior of the Hilbert cube C(X), proved by recognizing the complement as an F-sigma-absorber; the separating members form a D_2(F-sigma)-absorber.

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Hyperspaces of continua with connected boundaries in pi-Euclidean Peano continua

Pawel Krupski (Wroclaw University of Science and Technology, arXiv 1806.10691, math.GN, MSC primary 57N20) identifies the topological type of a particular family of subcontinua inside a hyperspace. F…