(1) connected (2) path connected (3) locally connected (4) locally path connected (5) compact (6) limit point compact (7) locally compact Hausdorff (8) Hausdorff (9) regular (10) completely regular (11) normal (12) first-countable (13) second-countable (14) Lindelöf (15) has a countable dense subset (16) locally metrizable (17) metrizable
(1) connected (2) path connected (3) locally connected (4) locally path connected (5) compact (6) limit point compact (7) locally compact Hausdorff (8) Hausdorff (9) regular (10) completely regular (11) normal (12) first-countable (13) second-countable (14) Lindelöf (15) has a countable dense subset (16) locally metrizable (17) metrizable
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 75E
Question
Help please!
Consider the following properties below, which one apply to a space: "R^ω in the box topology", also show the proof for each one please:
Transcribed Image Text:(1) connected
(2) path connected
(3) locally connected
(4) locally path connected
(5) compact
(6) limit point compact
(7) locally compact Hausdorff
(8) Hausdorff
(9) regular
(10) completely regular
(11) normal
(12) first-countable
(13) second-countable
(14) Lindelöf
(15) has a countable dense subset
(16) locally metrizable
(17) metrizable
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