Let (X, T) and (Y, T1) be topological spaces and f a mapping of X into Y. If (X, T) is a discrete space, prove that f is continuous. Let (X, T) and (Y, T1) be topological spaces and ƒa mapping of X into Y. If (Y,T1) is an indiscrete space, prove that f is continuous.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 8E
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topology
Let (X, T) and (Y, T1) be topological spaces and f a mapping of X into Y. If
(X, T) is a discrete space, prove that f is continuous.
Let (X, T) and (Y, T1) be topological spaces and ƒa mapping of X into Y. If
(Y,T1) is an indiscrete space, prove that f is continuous.
Transcribed Image Text:Let (X, T) and (Y, T1) be topological spaces and f a mapping of X into Y. If (X, T) is a discrete space, prove that f is continuous. Let (X, T) and (Y, T1) be topological spaces and ƒa mapping of X into Y. If (Y,T1) is an indiscrete space, prove that f is continuous.
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