query: Alternatives to Calabi-Yau spaces?
positive_passages.docid: 156382
positive_passages.text: Why is Compactification restricted to Toroids, Calabi-Yau et al?
negative_passages.docid: 141299
negative_passages.text: Alternative set theories
negative_passages.docid: 64084
negative_passages.text: Existence of a simple closed curve which is not null-homotopic
negative_passages.docid: 30597
negative_passages.text: Morphism that is not a mapping
negative_passages.docid: 37841
negative_passages.text: Product of quotient maps and quotient space that is not Hausdorff
negative_passages.docid: 74024
negative_passages.text: Higher dimensional equivalent of complex numbers
negative_passages.docid: 147287
negative_passages.text: Is it possible to construct a metric in $\mathbb{R}^n $ s.t. it does not induce CONVEX balls?
negative_passages.docid: 70543
negative_passages.text: Does an uncountable discrete subspace of the reals exist?
negative_passages.docid: 95234
negative_passages.text: Quasi-components in compact space
negative_passages.docid: 122410
negative_passages.text: Can one build a homology theory using submanifolds and their boundaries?
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
negative_passages.docid: 129623
negative_passages.text: A shrinking map that is not a contraction no fixed point.
negative_passages.docid: 1491
negative_passages.text: Correct spaces for quantum mechanics
negative_passages.docid: 132025
negative_passages.text: Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
negative_passages.docid: 64375
negative_passages.text: Non-Metrizable Topological Spaces
negative_passages.docid: 87983
negative_passages.text: Examples of Separable Spaces that are not Second-Countable
negative_passages.docid: 147961
negative_passages.text: Characterizing simply connected spaces