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Algebraic Topology MTH 477 For Master of Mathematics By

Algebraic Topology MTH 477 For Master of Mathematics By

Algebraic Topology MTH 477 For Master of Mathematics By. Dr. SOHAIL IQBAL Assistant Professor Department of Mathematics, CIIT Islamabad. Lecture # 3 Homotopy Topology, some basics Homotopy. Topology.

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357 views • 33 slides
Conservation Planning for Lincoln County and Indian/Howards Creek

Conservation Planning for Lincoln County and Indian/Howards Creek

Conservation Planning for Lincoln County and Indian/Howards Creek. Conservation Values Considered. Size of parcels In voluntary or enhanced voluntary agricultural district Proximity to impaired streams (303(d) streams) Linear feet of a stream on a property Distance to a protected property

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MA4266 Topology

MA4266 Topology

Lecture 15. Tuesday 30 March 2010. MA4266 Topology. Wayne Lawton Department of Mathematics S17-08-17, 65162749 matwml@nus.edu.sg http://www.math.nus.edu.sg/~matwml/ http://arxiv.org/find/math/1/au:+Lawton_W/0/1/0/all/0/1. Chains and Maximal Elements. Assume that.

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263 views • 11 slides
MA4266 Topology

MA4266 Topology

Lecture 11. MA4266 Topology. Wayne Lawton Department of Mathematics S17-08-17, 65162749 matwml@nus.edu.sg http://www.math.nus.edu.sg/~matwml/ http://arxiv.org/find/math/1/au:+Lawton_W/0/1/0/all/0/1. Basics. Theorem 6.11: A subset of. is compact iff it is. closed and bounded.

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Continuous functions

Continuous functions

Continuous functions. Definition: Let f be a function from a metric space (X,d1) to a metric space (Y,d2) then we say that f is a continuous function at x=a if : for each open set G in Y such that f(a) ? G, then f -1 (G) is open set in X. f is continuous if it continuous at all a? X. Example:

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Compact Spaces: Definition:

Compact Spaces: Definition:

Compact Spaces: Definition: Let (x,d) be a metric space and A ? X , {G i? I } be a family of open sets such that A ?. then we say that {G i ? I } be an open cover of A. If I is a finite set then we that {Gi ? I } a finite open cover of A. Definition:

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ASSIGENMENT II B.SC.II UNIT I

ASSIGENMENT II B.SC.II UNIT I

ASSIGENMENT II B.SC.II UNIT I. TOPOLOGY OF REAL NUMBERS. Prove that arbitrary union of open sets is open. Prove that the set of rationals is not order complete. Prove that a set A is compact iff every open cover of A has finite subcover .

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