Compact set | Compact space | continuous image of a compact space is compact | topology |

In this video you will learn Definitions of Open cover, Compact set, Compact space and also
learn a Theorem :- continuous image of a compact space is compact in Topology
#mscmathematics #topology
TOPOLOGY LINKS:-
Lecture-1 |Definition of Topology
• Topology || Definition...
Lecture-2 |Examples of Topology
• Topology | Examples of...
Lecture-3 |Discrete & indiscrete topology
• Topology | Discrete & ...
Lecture-4 |Intersection of two topologies on X is also a Topology on X
• Topology | Intersectio...
Lecture-5 | Union of topologies need not be a topology
• Topology | Union of to...
Lecture-6 |Subspace Topology Definition | Relative Topology
• Topology | Subspace To...
Lecture-18 Open & Continuous mapping |
• Open & Continuous mapp...
Compact set | Compact space |Topology
• Compact set | Compact ...
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REAL ANALASIS LINKS
Leture-1 |Real number system in real analysis
• Real number system in ...
Leture-2 |Metric space in real analysis
• Metric space in real a...
Leture-3 |Usual metric on R defination
• Usual metric on R defi...
Leture-4|Openball and closedball defination
• Openball and closedbal...
Leture-5|neighborhood of a point in metric space
• neighborhood of a poin...
Leture-6|limit point of a set,isolated point,closed set in Metric space
• limit point of a set,i...
Leture-7|Example of closed set in metric space
• Example of closed set ...
Leture-8|Example of closed set and isolated point in metric space
• Example of closed set ...
Leture-9|interior point of a set,interior of E,open set
• interior point of a se...
Leture-10|is neighbourhoods are open sets in any metric space
• is neighbourhoods are ...
Leture-11|Theorem gives an equivalent definition of limit point of a set
• Theorem gives an equiv...
Leture-12|Generalized demorgan laws
• Generalized demorgan l...
Leture-13 |If E is an open set,is compliment of E is closed set in metric space ?
• If E is an open set ,i...
Leture-14 |F is a closed set iff compliment of F is an open set
• F is a closed set iff ...
Leture-15 |Arbitary union of open sets is an open set
• Arbitary union of open...
Leture-16 |intersection of finite number of open sets is an open set
• intersection of finite...
Leture-17 |Arbitary intersection of opensets need not be an open set
• Arbitary intersection ...
Leture-18 |Clouser of a set definition
• Clouser of a set defin...
Leture-19 |Clouser of E is closed set in metric space X
• Clouser of E is closed...
Leture-20 |Subspace of a Metric space in telugu
• Real analysis | Subspa...
Leture-21 |Subspace of a Metric space is a Metric space
• Real analysis | Subspa...

[@aanyapatel1978]

మంచి వివరణ Superb 👌👌

[@krishnasai6050]

Good explanation

[@pavanivishnubruhathi6368]

Noted down thank u

[@maheshkumara188]

Every compact space is countably compact

[@srieducationclassesintelug3350]

Yes, Every compact space is countably compact Reason: every open cover(either finite or infinite) of a topological space X has a finite subcover