MCS 451, Topology (4 0 4)
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Weeks
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Course Topics
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1
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Introduction; Sets, Relations, Ordering, Partial Ordering
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2
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Topological spaces; definitions, accumulation points, closure of a set, interior, exterior and boundary, convergent sequences, coarser and finer topologies |
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3
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Basis and Sub bases, metric topologies
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4
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Topologies generated by classes of sets
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5
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Continuous and closed functions, homeomorphisms
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6
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The identification Topology and Quotient spaces
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7
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Separation axioms; T1 -spaces, Hausdorff spaces, Regular spaces,
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8
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Normal spaces, Urysohn's lemma, completely regular spaces
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9
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Compactness; covers, compactness and Hausdorff spaces, sequentially compact sets, local compactness
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10
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Connectedness
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11
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Complete metric spaces
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12
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Normed and function spaces, Ascoli’s theorem
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13
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Nets and Filters |
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14
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Review
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