Real Analysis | The continuous image of a compact set.

We look at some topological implications of continuity. In particular, we prove that the continuous image of a compact set of real numbers is compact and use this to prove the extreme value theorem. Please Subscribe: youtube.com/michaelpennmath?sub_confirmation=1 Merch: teespring.com/stores/michael-... Personal Website: www.michael-penn.net/ Randolph College Math: www.randolphcollege.edu/mathematics/ Randolph College Math and Science on Facebook: www.facebook.com/randolph.science/ Research Gate profile: www.researchgate.net/profile/Michael_Penn5 Google Scholar profile: scholar.google.com/citations?user=W5wkSxcAAAAJ&hl=… If you are going to use an ad-blocker, considering using brave and tipping me BAT! brave.com/sdp793 Buy textbooks here and help me out: amzn.to/31Bj9ye Buy an amazon gift card and help me out: amzn.to/2PComAf Books I like: Abstract Algebra: Judson(online): abstract.ups.edu/ Judson(print): amzn.to/2Xg92wD Dummit and Foote: amzn.to/2zYOrok Gallian: amzn.to/2zg4YEo Artin: amzn.to/2LQ8l7C Differential Forms: Bachman: amzn.to/2z9wljH Number Theory: Crisman(online): math.gordon.edu/ntic/ Strayer: amzn.to/3bXwLah Andrews: amzn.to/2zWlOZ0 Analysis: Abbot: amzn.to/3cwYtuF How to think about Analysis: amzn.to/2AIhwVm Calculus: OpenStax(online): openstax.org/subjects/math OpenStax Vol 1: amzn.to/2zlreN8 OpenStax Vol 2: amzn.to/2TtwoxH OpenStax Vol 3: amzn.to/3bPJ3Bn My Filming Equipment: Camera: amzn.to/3kx2JzE Lense: amzn.to/2PFxPXA Audio Recorder: amzn.to/2XLzkaZ Microphones: amzn.to/3fJED0T Lights: amzn.to/2XHxRT0 White Chalk: amzn.to/3ipu3Oh Color Chalk: amzn.to/2XL6eIJ

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