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Abstract: This paper sets forth three mismatch properties, strictly ordered in strength, about sewings of crumpled n-cubes. The strongest is a sufficient but not a necessary condition for a sewing to yield , and the weakest, a necessary but not sufficient one. We show that when both crumpled cubes satisfies the Disjoint Disks Property, then the weakest property implies the sewing yields , and we also show that the intermediate property leads to the same conclusion when just one of the crumpled cubes possesses the Disjoint Disks Property. In addition, we develop examples that confirm sharpness of the relevant Disjoint Disks conditions. [Copyright &y& Elsevier]

Abstract: In this paper we show that any graph map without periodic points has only one minimal set. We describe a class of graph maps without periodic points. Our main result is to give a structure theorem of graph maps without periodic points, which states that any graph map without periodic points must be topologically conjugate to one of the described class. In addition, we give some applications of the structure theorem. [Copyright &y& Elsevier]

A quandle is a set with a self-distributive binary operation satisfying a certain condition. Here we construct a monoid (a semi-group with the identity) associated with a quandle. This monoid has a structure of a quandle, which contains the original quandle as a sub-quandle. We call it the enveloping monoidal quandle. The purpose of this paper is to introduce the notion of the enveloping monoidal quandle, and to investigate it. [Copyright &y& Elsevier]

In this paper, we prove the following: Let Y be a perfect paracompact (hereditarily Lindelöf) space and {Xn: n∈ω} be a countable collection of Čech-scattered paracompact (Lindelöf) spaces, then the product Y×∏n∈ωXn is paracompact (Lindelöf). [Copyright &y& Elsevier]