OPEN PROBLEMS IN TOPOLOGY

ContentsxiIV Topology and Algebraic Structures 311Problems on Topological Groups and other Homogeneous Spacesby W. W. Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3130. Introduction and Notation . . . . . . . . . . . . . . . . . . . . . . . 3151. Embedding Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 3162. Proper Dense Subgroups . . . . . . . . . . . . . . . . . . . . . . . . 3263. Miscellaneous Problems . . . . . . . . . . . . . . . . . . . . . . . . . 328References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338Problems in Domain Theory and Topologyby J. D. Lawson and M. Mislove . . . . . . . . . . . . . . . . . . . . . 3491. Locally compact spaces and spectral theory . . . . . . . . . . . . . . 3522.TheScottTopology ...........................3543.FixedPoints ...............................3574. Function Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3585. Cartesian Closedness . . . . . . . . . . . . . . . . . . . . . . . . . . 3606. Strongly algebraic and finitely continuous DCPO’s . . . . . . . . . . 3627. Dual and patch topologies . . . . . . . . . . . . . . . . . . . . . . . 3648. Supersober and Compact Ordered Spaces . . . . . . . . . . . . . . . 3679.Adjunctions ...............................36810. Powerdomains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370V Topology and Computer Science 373Problems in the Topology of Binary Digital Imagesby T. Y. Kong, R. Litherland and A. Rosenfeld . . . . . . . . . . . . 3751. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3772. Two-Dimensional Thinning . . . . . . . . . . . . . . . . . . . . . . . 3773. Three-Dimensional Thinning . . . . . . . . . . . . . . . . . . . . . . 3814.OpenProblems..............................383Acknowledgement ..............................384References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384On Relating Denotational and Operational Semantics for ProgrammingLanguages with Recursion and Concurrencyby J.-J. Ch. Meyer and E. P. de Vink . . . . . . . . . . . . . . . . . . 387Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 390Operational Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394Denotational Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 396Equivalence of O and D ...........................398