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ON CB-COMPACT, COUNTABLY CB-COMPACT AND CB
... Proposition 1.8. If M is a CB-compact subspace of a space X , then M is also a CB-compact subset of X . Proof of this proposition easily follows if we use the relation @X A @M (A \ M ) whenever M X and A X , see e.g. Lemma 1.11 from [9]. Lemma 1.9. If U M X , then @X U @M U [ @X M . Proo ...
... Proposition 1.8. If M is a CB-compact subspace of a space X , then M is also a CB-compact subset of X . Proof of this proposition easily follows if we use the relation @X A @M (A \ M ) whenever M X and A X , see e.g. Lemma 1.11 from [9]. Lemma 1.9. If U M X , then @X U @M U [ @X M . Proo ...
on topological chaos
... Example 1.21. [15] There exists f ∈ C(X), with X Cantor set, such that h(f ) > 0 and X is minimal so that ωf is constant. Example 1.22. [10] There exists f ∈ C(X), with X Cantos set, such that f is Devaney chaotic, h(f ) = ∞ and ωf is everywhere discontinuous. Example 1.23. [11] There exists f ∈ C(X ...
... Example 1.21. [15] There exists f ∈ C(X), with X Cantor set, such that h(f ) > 0 and X is minimal so that ωf is constant. Example 1.22. [10] There exists f ∈ C(X), with X Cantos set, such that f is Devaney chaotic, h(f ) = ∞ and ωf is everywhere discontinuous. Example 1.23. [11] There exists f ∈ C(X ...
3-manifold
![](https://commons.wikimedia.org/wiki/Special:FilePath/3-Manifold_3-Torus.png?width=300)
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.