Is the Mapping f:\mathbb{Q}_p \rightarrow \mathbb{R} Continuous?

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Homework Help Overview

The discussion revolves around the continuity of the mapping f: ℚₚ → ℝ, where f(x) = x. Participants explore the implications of defining continuity in the context of p-adic and real number metrics.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants examine the definition of continuity and its application to the mapping between p-adic and real numbers. There are questions about the well-defined nature of the function and whether it can be continuous given the differing metrics.

Discussion Status

The discussion is active, with participants questioning the assumptions behind the mapping and its continuity. Some have provided examples to illustrate their points, while others seek clarification on specific aspects of the definitions involved.

Contextual Notes

There are concerns about the validity of the function f as a mapping from ℚₚ to ℝ, particularly regarding how p-adic numbers are represented in the reals. The discussion also highlights the necessity of proving continuity or lack thereof through specific examples and metrics.

  • #31
It really is easier to think of the closed sets, you know, A set is closd in the finite complement topology iff it is finite or the whole space or the empty set.

Thankyou Matt. Using closed sets the continuity is easier to prove because of the topology.
 

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