# Problems

From hyperspacewiki

The Houston Problem Book (pdf)

The Houston Problem Book (wiki)

Open problems in continuum theory (html)

Open problems in continuum theory (wiki)

Pavel Pyrih Problem Book (html)

Pavel Pyrih Problem Book (wiki)

Inverse limits with upper semi-continuous bonding functions, problems and some partial solutions (pdf)

Inverse limits with upper semi-continuous bonding functions problems (wiki)

#### Problems from the book A. Illanes and S. B. Nadler, Jr., *Hyperspaces: Fundamentals and Recent Advances*, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1999.

Page |
Problem |
Solved? |

p.205 | 23.2: Let $Y$ be a connected, locally connected metric space. Then does Theorem 23.1 hold for CLC(Y)? |
? |

p.210 | 24.7: Is Theorem 24.6 true without the hypothesis that $X$ is locally connected? |
? |

p.211 | 24.8: Is $F(X)$ unicoherent for every continuum $X$? |
? |

p.214 | 24.14: Give necessary and/or sufficient conditions for a continuum $X$ to have a confluent Whitney map. |
? |

p.214 | 24.15: If $X$ is an hereditarily indecomposable continuum, does $2^X$ have monotone Whitney maps? |
? |

p.214 | 24.16: If $X$ is an hereditarily indecomposable continuum, can $2^X$ have monotone Whitney maps? |
? |

p.215 | 24.18: Let $X$ be a continuum. What topological properties do the Whitney levels of open Whitney maps for $2^X$ have? |
? |

p.233 | 27.2:Is there a strong Whitney-reversible property which is not a sequential strong Whitney-reversible property? |
Solved |

p.250 | 33.13: Is the property of being uniformly pathwise connected a Whitney property? Is this property a Whitney-reversible property (strong Whitney-reversible property, sequential strong Whitney-reversible property)? |
Solved |

#### Problems from the book S. B. Nadler, Jr., *Hyperspaces of sets*, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, Inc., New York, N.Y., 1978.

Page |
Problem |
Solved? |