In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is an isolated element in the graph of triangulations of the point configuration. It has been a central open question in polytope combinatorics in the last decade whether point configurations exist for...

Inverse model based multiobjective evolutionary algorithm aims to sample candidate solutions directly in the objective space, which makes it easier to control the diversity of non-dominated solutions in multiobjective optimization. To facilitate the process of inverse modeling, the objective space is partitioned into several subregions by predefining a set of reference vectors. In the previous ...

Topological groups whose underlying spaces are basically disconnected, F-, or F′-spaces but not P-spaces considered. It is proved, in particular, that the existence of a Lindelöf disconnected topological group which P-space equivalent to Boolean countable pseudocharacter, free and Abelian zero-dimensional non-P-spaces never F′-spaces, F′-group selective ultrafilters on ω.

It is proved that there is no structure of left (right) cancelative semigroup on [L]-dimensional universal space for the class of separable compact spaces of extensional dimension ≤ [L]. Besides, we note that the homeomorphism group of [L]-dimensional space whose nonempty open sets are universal for the class of separable compact spaces of extensional dimension ≤ [L] is totally disconnected.

We deal with the new class of pre-ℐ-regular pre-ℐ-open sets in which the notion of pre-ℐ-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-ℐ-disconnectedness, locally pre-ℐ-indiscreetness, and pre-ℐ-regular sets by utilizing the notion of pre-ℐ-open and pre-ℐ-closed sets by which we obtain some eq...

The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...