Presentation Title

The Topological Structure of the Biquaternionic Projective Point

Start Date

12-11-2016 11:00 AM

End Date

12-11-2016 11:15 AM

Location

HUB 355

Type of Presentation

Oral Talk

Abstract

The biquaternions B are a noncommutative algebra that contains zero divisors. It has been previously shown that a quotienting process can be employed to construct the biquaternionic projective point BP0 from B. It is known that BP0 possesses a natural twistor structure that comes about from properties within its topology.1 While it is understood that the twistor structure arises from the quotient topology of BP0, the topology itself is not well understood. In this paper we seek to explore the topological structure of BP0. We will show that BP0 has an exotic topology that possesses many interesting properties due to the presence of a dense point in its structure. Here, we will begin by characterizing a basis for the topology which we will utilize to show that the dense point lies in every nonempty open subset of BP0. We then use this fact to show that BP0 is connected. Finally, we construct derived sets for arbitrary open and closed subsets of BP0, and show that every nonempty open subset is dense and every proper closed subset has an empty interior.

1. Agnew, A. F. (2003). The Twistor Structure of the Biquaternionic Projective Point. Advances in Applied Cliff ord Algebras, 13(2), 231-240.

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Nov 12th, 11:00 AM Nov 12th, 11:15 AM

The Topological Structure of the Biquaternionic Projective Point

HUB 355

The biquaternions B are a noncommutative algebra that contains zero divisors. It has been previously shown that a quotienting process can be employed to construct the biquaternionic projective point BP0 from B. It is known that BP0 possesses a natural twistor structure that comes about from properties within its topology.1 While it is understood that the twistor structure arises from the quotient topology of BP0, the topology itself is not well understood. In this paper we seek to explore the topological structure of BP0. We will show that BP0 has an exotic topology that possesses many interesting properties due to the presence of a dense point in its structure. Here, we will begin by characterizing a basis for the topology which we will utilize to show that the dense point lies in every nonempty open subset of BP0. We then use this fact to show that BP0 is connected. Finally, we construct derived sets for arbitrary open and closed subsets of BP0, and show that every nonempty open subset is dense and every proper closed subset has an empty interior.

1. Agnew, A. F. (2003). The Twistor Structure of the Biquaternionic Projective Point. Advances in Applied Cliff ord Algebras, 13(2), 231-240.