Moniker1998
Moniker1998
https://en.wikipedia.org/wiki/Shrinking_space A property for which it would be nice to have examples for. Implies: normal, countably paracompact Implied by: normal metacompact
Hello, I've recently been browsing pi-base, and could not find a good example of a space that would be pseudocompact, not compact, $T_1$, and exhaustible by compact sets. The space...
As the title. In one of the articles $\aleph_0$-spaces on pi-base reference to https://topology.pi-base.org/properties/P000179/references that is $\aleph_0$-spaces by E. Michael, there's also contained a result that dual of a separable...
https://topology.pi-base.org/spaces?q=%3Fhomogenous Spaces which are homogeneous: https://topology.pi-base.org/spaces/S000015 (obvious from definition) https://topology.pi-base.org/spaces/S000017 (obvious from definition) https://topology.pi-base.org/spaces/S000018 (product of homogeneous spaces) https://topology.pi-base.org/spaces/S000019 (obvious from definition since R is) https://topology.pi-base.org/spaces/S000032 (standard result, see e.g....
Lets call (P) to be: every locally finite open cover has a finite subcover. Its clear that (P) implies pseudocompactness, and for completely regular spaces the converse holds. Does (P)...
https://topology.pi-base.org/spaces/S000196 Clearly $\omega_1$ is a subspace of the long circle so its not $T_6$ Moreover, any its proper subspaces is a subspace of a LOTS, so normal.
Since R/Z [S000139](https://topology.pi-base.org/spaces/S000139) is a continuous image of a separable metrizable space R, it's a cosmic space.
This is follows directly from Corollary 7.10 in $\aleph_0$-spaces by E. Michael.
Bing's example H is a space that's $T_6$ but not collectionwise normal. https://www.cambridge.org/core/services/aop-cambridge-core/content/view/48C1A50A9E249D05BD7054529F93BAA1/S0008414X00030923a.pdf/metrization-of-topological-spaces.pdf https://dantopology.wordpress.com/2014/02/02/bings-example-h/ Since there is no such example in pi-base, it'd be nice to include it.
The current definition of Novak space is wrong and needs to be fixed. Indeed, if we were to take $P_A = \emptyset$ for all $A$ then we would obtain $\mathbb{N}$....