We demonstrate that while the intersection of a finite number of open sets in $\mathbb R$ remains open in $\mathbb R$, the same cannot be universally said for intersections involving an infinite number of open sets. An illustrative example is presented to highlight this distinction.
https://doi.org/10.31219/osf.io/4kjdq
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 279, 2023 [LB]
We prove some theorems in topology using the fewest number of symbols at each step. Our purpose is pedagogical.
https://doi.org/10.31219/osf.io/wn24y
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 4, Article 267, 2022 [KM]
This is an introductory collection of theorems in topology.
https://doi.org/10.31219/osf.io/zm56w
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 4, Article 260, 2022 [KE]
[knowledge base]
METRIZABLE TOPOLOGICAL SPACE and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/f8vez
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 205, 2021 [IB]
[knowledge base]
PRESHEAF and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/2y5s4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 201, 2021 [HY]
[microreview]
We prove the Banach-Tarski decomposition paradox applied to a circle.
https://doi.org/10.31219/osf.io/mh5gx
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 142, 2020 [FN]
[microresearch]
Supposedly, matter falls inside the black hole whenever it reaches its event horizon. The Planck scale, however, imposes a limit on how much matter can occupy the center of a black hole. It is shown here that the density of matter exceeds Planck density in the singularity, and as a result, spacetime tears apart. After the black hole is formed, matter flows from its center to its border due to a topological force; namely, the increase on the tear of spacetime due to its limit, until it reaches back to the event horizon, generating the firewall phenomenon. We conclude that there is no spacetime inside black holes. We propose a solution to the black hole information paradox.
https://doi.org/10.31219/osf.io/js7rf
Open Physics Collaboration
Op. J. Math. Phys.
Volume 2, Article 78, 2020 [DA]
[original insight]
This is a thought experiment with the following conjecture: bubbles of spacetime void alter the gravitational field of the galaxy and might explain the dark matter phenomenon.
https://doi.org/10.31219/osf.io/w7m3q
Open Physics Collaboration
Op. J. Math. Phys.
Volume 1, Article 33, 2019 [BG]
[original idea]
These are the first steps, I believe, that can contribute to the understanding of the most fundamental nature of spacetime.
https://doi.org/10.31219/osf.io/4mbxq
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 1, Article 16, 2019 [AP]
[original idea]
This article connects the following concepts: the “interior of a black hole” with the “void of spacetime,” by means of a thought experiment.
https://doi.org/10.31219/osf.io/awfx8
Open Physics Collaboration
Op. J. Math. Phys.
Volume 1, Article 1, 2019 [AA]
Open Journal of Mathematics and Physics 